Strange dibaryon system producedin the d(π +, K +) reaction at J-PARC

A dissertation
by

Yudai Ichikawa
Submitted to
Department of Physics, Kyoto University
in partial fulfillment of the requirements
for the Degree of Doctor of Science

February, 2015

Abstract
The strange dibaryon systems (strangeness S = −1 and baryon number B = 2)
such as a K̄N N system, in which a bound state of K − pp is expected to exist, areexperimentally not well explored, yet. We have searched for a strange dibaryon systems
by using the π + d → K + X reaction at 1.69 GeV/c in the laboratory angles between
2◦ and 16◦ . We achieved the missing-mass resolution of 2.7 MeV/c2 (FWHM). This
experiment was carried out at the K1.8 beam line of the J-PARC hadron experimental
facility. The K1.8 beam line spectrometer and the SKS spectrometer were used with agood momentum resolution of ∆p/p ∼ 10−3 to measure π + and K + momenta.
In this reaction, Λ(1405) hyperon resonance is expected to be produced as a doorway to form the K − pp through the Λ∗ p → K − pp process. However, most of the
produced Λ(1405)’s would escape from deuterons without secondary reactions. Therefore, coincidence of high-momentum (> 250 MeV/c) proton(s) in large emission angles(39◦ < θlab. < 122◦ ) is requested to enhance the signal-to-background ratio. It is becausesuch proton(s) can be produced from the K − pp but not from the quasi-free hyperon
production (background).
We have measured the inclusive missing-mass spectrum at this beam energy in highstatistics and high energy resolution for the first time. The present data covers witha wide missing-mass range from the Λ mass threshold to the Λ(1405)/Σ(1385) region.
While a gross structure is well understood with a simple quasi-free picture based on
the known elementary processes, we have observed two distinct deviations; one peculiar
enhancement at 2.13 GeV/c2 is due to the ΣN cusp, and the other notable feature is a
“shift” of a broad bump structure, mainly originating from hyperon resonance productions of Λ(1405) and Σ(1385)+/0 .
We have measured a mass distribution of a “K − pp”-like structure in the π + d →+K “K − pp”, “K − pp”→ Σ0 p mode in a two-proton coincidence analysis, for the firsttime. By fitting the mass distribution with a relativistic Breit Wigner function, the+21
2mass and width have been evaluated to be 2275 +17−18 (stat.) −30 (syst.) MeV/c and
+66
+87
−
162 −45 (stat.) −78 (syst.) MeV, respectively. It corresponds to the K pp binding energy+30of 95 +18
−17 (stat.) −21 (syst.) MeV.

Contents
1 Introduction
1.1 K̄N interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Λ(1405) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 K̄-nucleus interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Kaonic nuclei: Experiments and Theory . . . . . . . . . . . . . . . . . .
1.4.1 Past experiments of the K − pp . . . . . . . . . . . . . . . . . . . .
1.4.2 Current situation of the K − pp . . . . . . . . . . . . . . . . . . . .
1.4.3 Theoretical studies of the K − pp . . . . . . . . . . . . . . . . . . .
1.5 J-PARC E27 experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Thesis composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Experiment
2.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 J-PARC and hadron experimental facility . . . . . . . . . . . . . . . . . .
2.3 K1.8 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 K1.8 beam line spectrometer . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Superconducting kaon spectrometer (SKS) . . . . . . . . . . . . . . . . .
2.6 Liquid hydrogen and deuterium target . . . . . . . . . . . . . . . . . . .
2.7 Range counter array (RCA) . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Data-acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Analysis I - inclusive analysis
3.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Analysis of π + beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Identification of triggered beam particles . . . . . . . . . . . . . .
3.2.2 BC1 and BC2 local tracking . . . . . . . . . . . . . . . . . . . . .
3.2.3 BC3 and BC4 local tracking . . . . . . . . . . . . . . . . . . . . .
3.2.4 Beam momentum reconstruction . . . . . . . . . . . . . . . . . .
3.2.5 Eﬃciency for the π + beam . . . . . . . . . . . . . . . . . . . . . .
3.3 Analysis of emitted K + . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 SDC1 and SDC2 local tracking . . . . . . . . . . . . . . . . . . .
3.3.2 SDC3 and SDC4 local tracking . . . . . . . . . . . . . . . . . . .
3.3.3 Momentum reconstruction of scattered particles . . . . . . . . . .

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CONTENTS
3.3.4 Eﬃciency for K + trigger counters . . . . . . . . . . . . . . . . .
3.3.5 Kaon identification in the SKS . . . . . . . . . . . . . . . . . . . .
3.4 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Momentum correction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Momentum correction of K + . . . . . . . . . . . . . . . . . . . . .
3.5.2 Momentum correction of π + and systematic error . . . . . . . . .
3.6 Missing-mass resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1 Data acquisition eﬃciency (ϵDAQ ) . . . . . . . . . . . . . . . . . .
3.7.2 Eﬃciency of the trigger bias (ϵtrig ) . . . . . . . . . . . . . . . . .
3.7.3 K + decay factor (fdecay ) . . . . . . . . . . . . . . . . . . . . . . .
3.7.4 Acceptance of the SKS . . . . . . . . . . . . . . . . . . . . . . . .
3.7.5 Systematic errors . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 The Σ+ production cross section . . . . . . . . . . . . . . . . . . . . . . .

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4 Analysis II - Coincidence analysis
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4.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 Velocity calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Gain calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.1 P ID parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4 Particle identification in RCA . . . . . . . . . . . . . . . . . . . . . . . . 108
4.4.1 Analysis for stopping layer istop = 2 ∼ 4 . . . . . . . . . . . . . . 108
4.4.2 Analysis for stopping layer istop = 1 . . . . . . . . . . . . . . . . . 109
4.4.3 Analysis for stopping layer istop = 5 . . . . . . . . . . . . . . . . . 111
4.5 Detection eﬃciency of RCA . . . . . . . . . . . . . . . . . . . . . . . . . 113
5 Experimental results and discussion
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5.1 Inclusive analysis: results and discussion . . . . . . . . . . . . . . . . . . 117
5.1.1 Inclusive missing-mass spectra of the d(π + , K + ) reaction . . . . . 117
5.1.2 Quasi-free processes in the d(π + , K + ) reactions . . . . . . . . . . 119
5.1.3 Discussion on inclusive spectra . . . . . . . . . . . . . . . . . . . . 124
5.2 Coincidence analysis: results and discussion . . . . . . . . . . . . . . . . 134
5.2.1 π coincidence analysis . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2.2 One-proton coincidence analysis . . . . . . . . . . . . . . . . . . . 135
5.2.3 Two-proton coincidence analysis . . . . . . . . . . . . . . . . . . . 137
5.2.4 Identification of final states in two-proton coincidence . . . . . . . 137
5.2.5 Cross section in two-proton coincidence . . . . . . . . . . . . . . . 140
5.2.6 Results on proton coincidence spectra . . . . . . . . . . . . . . . . 143
5.2.7 Discussion on proton coincidence spectra . . . . . . . . . . . . . . 146
6 Conclusion

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A BH1 filter tracking

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B Accuracy of time oﬀset of RCA

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C ΣN cusp for two-proton coincidence analysis

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D Two-proton coincidence analysis using the EX spectrum

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List of Figures
The hadron spectrum of a strangeness −1 and baryon number B = 2
systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1−
1.2 The low energy K p scattering data and the curves calculated from the
M -matrix parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.3 Comparison of the ∆E1s ’s and Γ1s ’s of the kaonic hydrogen together withrecent theoretical calculated values. . . . . . . . . . . . . . . . . . . . .
4
1.4 The K − p → K − p forward scattering amplitude extrapolated to the subthreshold region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.5 Comparison between the measured masses and the predicted one from theconstituent quark model of the strangeness S = −1 negative parity baryons. 6
1.6 The level-shifts and widths of the K − atom with the best-fit density dependent optical potentials. . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.7 Comparison between the DWIA calculation of the 1sΛ hypernuclear formation rates in stopped K − reaction on several p-shell targets and measured
values from the FINUDA Collaboration . . . . . . . . . . . . . . . . . . .
8
−
−
4
4
1.8 The missing mass spectra of the He(Kstopped , p) and He(Kstopped , n) reactions obtained by KEK E549 experiment. . . . . . . . . . . . . . . . . 10
1.9 The Λp invariant mass spectrum obtained from the FINUDA experiment. 11
1.10 The deviation spectrum (DEV) of the of missing-mass spectrum of K +constructed from the DISTO experiment. . . . . . . . . . . . . . . . . . . 12
1.11 The (ppπ − ) invariant-mass spectrum corresponding to the Λp state obtained from the OBELIX experiment. . . . . . . . . . . . . . . . . . . . . 13
1.12 The d(γ, K + π − ) missing-mass spectrum of the LEPS experiment. . . . . 14
1.13 The obtained (ΛK + , pK + , pΛ) invariant mass spectra with the solutionof PWA evaluated from HADES experiment. . . . . . . . . . . . . . . . . 15
1.14 The semi-inclusive 3 He(K − , n) missing mass spectrum with estimatedbackgrounds of the J-PARC E15 experiment. . . . . . . . . . . . . . . . . 16
1.15 Summary of the calculated binding energy and width together with theexperimental values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.16 The Σ± π ∓ invariant mass spectrum and the angular distribution of
Λ(1405) measured by the old hydrogen bubble chamber experiment. . . 21
1.1

2.1
2.2
2.3
2.4

Schematic view of J-PARC . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of hadron experimental facility as of 2012. . . . . . . . .
Schematic view of K1.8 Beam line. . . . . . . . . . . . . . . . . . . . . .
Typical beam momentum distribution of π + in the present experiment. .
6

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LIST OF FIGURES
2.5 Typical beam profile of this experiment. . . . . . . . . . . . . . . . . . .
2.6 Schematic view of K1.8 beam spectrometer. . . . . . . . . . . . . . . . .
2.7 Schematic view of GC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Schematic view of BH1. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Schematic view of BH2. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Schematic view of tracking chambers of K1.8 beam line spectrometer. . .
2.11 Schematic view of the SKS. . . . . . . . . . . . . . . . . . . . . . . . . .
2.12 Schematic view of TOF. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 Threshold and refractive index for Čerenkov radiation as a function of the
momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14 Schematic view of LAC. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.15 Schematic view of LC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Schematic view of BVH. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.17 Typical trajectories of the background particles. . . . . . . . . . . . . . .
2.18 The cell structure of SDC3, 4. . . . . . . . . . . . . . . . . . . . . . . . .
2.19 Schematic view of the liquid hydrogen and deuterium target. . . . . . . .
2.20 The scatter plot between momentum and scattering angle in xz plane ofproton for the background and K − pp. . . . . . . . . . . . . . . . . . . .
2.21 Schematic view of RCA. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.22 Schematic view of one unit of range counter array and the range as afunction of β for the pion and proton. . . . . . . . . . . . . . . . . . . . .
2.23 Trigger logic diagram of this experiment. . . . . . . . . . . . . . . . . . .
2.24 The selected TOF and LC segments region with the matrix trigger . . . .
2.25 The horizontal direction cosine at SDC3, 4 position for each hit combination of TOF and LC segment. . . . . . . . . . . . . . . . . . . . . . . . .
2.26 Typical accepted and rejected region of the mass trigger. . . . . . . . . .
2.27 Logic Scheme of the 2nd-level mass trigger . . . . . . . . . . . . . . . . .
2.28 The diagram of the data-acquisition system. . . . . . . . . . . . . . . . .

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3.1 Flow chart of the oﬄine analysis for inclusive (π + , K + ) spectrum. . . . . 59
3.2 Time-of-flight spectrum of the incident beam particles. . . . . . . . . . . 60
3.3 Typical reduced χ2 distribution of the BC1, 2 local tracking. . . . . . . . 62
3.4 Typical residual distribution of the BC1 layers. . . . . . . . . . . . . . . 62
3.5 Typical TDC distributions of BC3 and BC4. . . . . . . . . . . . . . . . . 63
3.6 A scatter plot between the drift time and the drift length of the BC3 layers. 64
3.7 Typical reduced χ2 distribution of the BC3, 4 local tracking. . . . . . . . 65
3.8 Typical residual distribution of the BC3 layers. . . . . . . . . . . . . . . 65
3.9 Typical distribution of the momentum of π + beam. . . . . . . . . . . . . 67
3.10 Typical reduced χ2 distribution of the K1.8 tracking. . . . . . . . . . . . 67
3.11 Summary of the ϵK18 of the χ2 cut value dependence. . . . . . . . . . . . 68
3.12 The y distribution at the BC4 position. . . . . . . . . . . . . . . . . . . . 69
3.13 A summary of fµ of χ2K18 track cut value. . . . . . . . . . . . . . . . . . . 70
3.14 The analysis eﬃciency of beam particles. . . . . . . . . . . . . . . . . . . 70
3.15 The reduced χ2 distribution of the SDC1, 2 and SDC3, 4 local tracking. . 72
3.16 Proton selection for the estimation of ϵSDC34 . . . . . . . . . . . . . . . . . 73
3.17 Initial momentum function of the SKS tracking. . . . . . . . . . . . . . . 74

8

LIST OF FIGURES
3.18 Typical reduced χ2 distributions of the SKS tracking. . . . . . . . . . . .
3.19 The SKS tracking eﬃciency as a function of scattering angle. . . . . . . .
3.20 Scatter plot between the horizontal direction cosine measured by SDC1,
2 and the flight time of BH2-TOF. . . . . . . . . . . . . . . . . . . . . .
3.21 Mass squared distributions for the outgoing particles. . . . . . . . . . . .
3.22 The mass square distribution for the p(π + , K + )Σ+ data. . . . . . . . . .
3.23 The distribution of the diﬀerence of the dx/dz (a) and dy/dz (b) between
the K1.8 and SKS tracking. . . . . . . . . . . . . . . . . . . . . . . . . .
3.24 The vertex distribution of x and y direction. . . . . . . . . . . . . . . . .
3.25 The summary of z-vertex resolution. . . . . . . . . . . . . . . . . . . . .
3.26 The vertex distribution of z direction. . . . . . . . . . . . . . . . . . . . .
3.27 The vertex cut eﬃciency. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.28 Scatter plots between the direction cosines and the missing mass ofp(π + , K + )Σ+ reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.29 The momentum diﬀerence measured by the K1.8 beam line and the SKS.
3.30 The missing-mass spectrum of the p(π + , K + ) reaction in the Σ+ (1385)
mass region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.31 The momentum diﬀerence after the correction. . . . . . . . . . . . . . . .
3.32 The momentum resolution of K1.8 beam line spectrometer and the SKS.
3.33 Comparison between (π, K) inclusive trigger data and the unbiased (π, K)
trigger data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.34 Eﬃciency of the Matrix trigger, Mass trigger and BVH accidental vetofactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.35 The obtained decay factor as a function of M Md . . . . . . . . . . . . . .
3.36 The acceptance table for the d(π + , K + ) at 1.69 GeV/c data. . . . . . . .
3.37 The acceptance table for the p(π + , K + ) at 1.69 GeV/c data. . . . . . . .
3.38 The systematic error of the eﬃciency correcting event by event. . . . . .
3.39 The total systematic error (∆ϵ/ϵ) for the double diﬀerential cross section.
3.40 The obtained missing-mass spectra (M Mp ) for the p(π + , K + )Σ+ . . . . .
3.41 Acceptance of SKS with the three kinematical lines of K + . . . . . . . . .
3.42 The diﬀerential cross section of Σ+ production at 1.58 GeV/c. . . . . . .
3.43 The diﬀerential cross section of Σ+ production at 1.69 GeV/c. . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6

A typical scatter plot of the ADC and flight time after the slewing correction of BH2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical scatter plot of the ADC and flight time after the slewing correction of RCA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical time diﬀerence spectrum between the up and down PMT’s of
the first layer of RCA. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical 1/β spectrum around the Σ production region compared withsimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical correlation plot between the normalized ADC values of the thirdlayer fourth layer of RCA. . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical obtained normalized ADC and simulated energy deposit spectraof the fourth layer of RCA for the stopping proton at this layer. . . . . .

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LIST OF FIGURES
A typical obtained normalized ADC and simulated energy deposit spectraof the second layer of RCA for the stopping proton at fourth layer. . . . .
4.8 The correlation between the normalized ADC values and the energy deposit fitted with the second polynomial. . . . . . . . . . . . . . . . . . .
4.9 A typical scatter plot between the energy deposit of the first layer and theP ID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 A typical χ2 distribution as a function of α. . . . . . . . . . . . . . . . .
4.11 A typical scatter plot between the 1/β and P ID for the istop = 2 ∼ 4events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12 A typical P ID spectra for the istop = 2 ∼ 4 events. . . . . . . . . . . . .
4.13 A typical scatter plot between the 1/β and energy deposit in the first layerof RCA and typical proton selection gate. . . . . . . . . . . . . . . . . . .
4.14 The eﬀective range for the pion and proton. . . . . . . . . . . . . . . . .
4.15 A typical scatter plot between P ID and energy deposit of the fifth layerof RCA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.16 The simulated correlation plot between produced angle and the momentum of proton and π + from the Σ+ decay. . . . . . . . . . . . . . . . . .
4.17 The obtained 1/β spectrum for the Seg1 and 4 of RCA in coincidence with
Σ+ production compared with the simulation. . . . . . . . . . . . . . . .
4.18 The π + coincidence probability of each segment of RCA compared withthe simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

4.7The obtained inclusive missing-mass spectra of the d(π + , K + ) reaction at
1.69 GeV/c for the M Md . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The obtained inclusive missing-mass spectra of the d(π + , K + ) reaction at
1.69 GeV/c for the M Mp . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 The momentum distribution of a nucleon inside of deuteron obtained fromthe Bonn Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Considered elementary diﬀerential cross sections of the two-body reaction
for the quasi-free processes. . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 The diﬀerential cross section of the Σ0 production for the forward scattering angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 A simulated diﬀerential cross section of the d(π + , K + ) reaction for thequasi-free processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 A simulated diﬀerential cross section of the d(π + , K + ) reaction of theRegion III. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 The missing-mass spectrum (M Md ) of the d(π + , K + ) reaction comparedwith the simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 The missing-mass spectrum (M Md ) for the fitting of ΣN cusp. . . . . . .
5.10 The obtained Λp invariant mass spectrum of the old experiment. . . . .
5.11 The contour plot of the χ2 of the fitting as a function of the peak position
and width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.12 A summary of the peak positions and widths from the fit with one
Lorentzian function by the author of Ref. [107]. . . . . . . . . . . . . . .
5.13 A summary of peak positions and widths from the fit with two Lorentzianfunctions by the author of Ref. [107]. . . . . . . . . . . . . . . . . . . . .

105
106
107
107
108
109
110
111
112
113
114
115

5.1

118
118
119
121
122
123
123
124
125
126
127
128
128

5.14 The obtained double diﬀerential cross section (M Md ) for each scattering
angle compared with the simulated spectra. . . . . . . . . . . . . . . . .
5.15 The obtained double diﬀerential cross section (M Mp ) for each scattering
angle compared with the simulated spectra. . . . . . . . . . . . . . . . .
5.16 The peak positions of the Y ∗ bump for each scattering angle obtained
from the present data and simulated spectra. . . . . . . . . . . . . . . . .
5.17 A comparison of the π coincidence spectra between data and simulation.
5.18 The detection eﬃciency of a proton for each segment of RCA. . . . . . .
5.19 The one proton coincidence and coincidence probability spectra for the
middle segment of RCA. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.20 The two protons coincidence and coincidence probability spectra. . . . .
5.21 Missing-mass squared spectra of X obtained from the two proton coincidence events in the reaction of the d(π + , K + pp)X. . . . . . . . . . . . . .
5.22 Detection eﬃciency of two protons for Λp and Σ0 p modes. . . . . . . . .
5.23 Detection eﬃciency of two protons for each mode as a function of M Md .
5.24 The double diﬀerential cross section for the Λp and Σ0 p final state modes
estimated from the fitting of MX2 . . . . . . . . . . . . . . . . . . . . . . .
5.25 The double diﬀerential cross section for the Λp and Σ0 p final state modes
fitted with the relativistic Breit Winger function. . . . . . . . . . . . . .
5.26 The contour plot of the χ2 of the fitting as a function of the mass andwidth of the “K − pp”-like structure. . . . . . . . . . . . . . . . . . . . .
5.27 Comparison of the double diﬀerential cross sections between the inclusive
spectrum and “K − pp”-like structure. . . . . . . . . . . . . . . . . . . . .
5.28 The one proton coincidence probability spectrum of the middle segmentof RCA with the interpreted spectrum. . . . . . . . . . . . . . . . . . .
5.29 Comparison of the binding energy and width of the K − pp. . . . . . . . .

131
132
133
134
135
136
137
139
141
141
142
143
144
146
147
148

A.1 Schematic view of BH1Filter. . . . . . . . . . . . . . . . . . . . . . . . . 155
A.2 Typical hit position gate of BH1Filter. . . . . . . . . . . . . . . . . . . . 155
B.1 The MX2 spectrum for each time-oﬀset condition compared with the simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
C.1 The double diﬀerential cross section for the Λp final state mode around2.13 GeV/c2 compared with the past experiment. . . . . . . . . . . . . . 159
D.1 Energy spectra of X obtained from the two proton coincidence events in
the reaction of the d(π + , K + pp)X. . . . . . . . . . . . . . . . . . . . . . . 161
D.2 The double diﬀerential cross section for the Λp and Σ0 p final state modes
estimated from the fitting of EX . . . . . . . . . . . . . . . . . . . . . . . 162

List of Tables
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

Design specifications of the K1.8 beam line spectrometer . . . . . . . . . 30
Specifications of the trigger counters of the K1.8 beam line spectrometer
30
Specifications of the trackers of the K1.8 beam line spectrometer . . . . . 33
Design specifications of the SKS spectrometer at the 2.36 T mode. . . . . 35
Specifications of the particle identification counters in the SKS spectrometer 37
Specifications of the drift chambers of the SKS. . . . . . . . . . . . . . . 43
Specifications of the liquid hydrogen and deuterium target. . . . . . . . . 44
Summary of the obtained data with diﬀerent combinations of experimental
targets, incident π + momenta Pbeam , and beam intensities. Nbeam means
the total number of π + beam irradiated on the target. . . . . . . . . . . . 56

3.1
3.2
3.3

The position resolution of each layer. . . . . . . . . . . . . . . . . . . . .
The position resolution of each layer. . . . . . . . . . . . . . . . . . . . .
The scattering-angle resolutions and the missing mass resolutions of theΣ+ production at 1.58 GeV/c data. . . . . . . . . . . . . . . . . . . . . .
The list of the experimental eﬃciency and systematic error for the common
factor (ϵcom ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4
5.1

The elementary total cross sections of hyperon productions.

61
64
89
95

. . . . . . . 120

Chapter 1
Introduction
A multi-hadron spectrum of strangeness S = −1 and baryon number B = 2 system
is displayed in Figure. 1.1. In the low mass region, there are ΛN (2.05 GeV/c2 ) andΣN (2.13 GeV/c2 ) systems which are composed in octet baryons. The Λ-nucleon systemforms bound states called Λ-hypernuclei starting from three baryon system of 3Λ H (p +n + Λ). The Λ single particle energy in nuclear matter is obtained to be about 30 MeV
from the study of Λ-hypernuclei. This system is the ground state of S = −1, B = 2
systems. The ΣN system is about 80 MeV heavier than the ΛN system. It has a boundstate of four baryons 4Σ He. In heavier systems, the ΣN interaction is repulsive, and there
would be no bound states.
K−pp bound state (?)Λ*N bound state (?)πΛN - πΣN
dibaryon (?)

8×8
ΛN

8×8
ΣN

2.1

Λ*N

10×8
πΣN Σ*N

πΛN

2.2

KNN

2.3
2.4
Mass Threshold [GeV/c2]

Figure 1.1: The hadron spectrum of a strangeness S = − 1 and baryon number B = 2
system.

In the higher mass region, there is an energy threshold composed of Σ(1385), which is+a decuplet baryon with J P = 23 and S = −1, and nucleon at 2.32 GeV/c2 . We can also1

2

CHAPTER 1. INTRODUCTION

see a threshold of Λ(1405) and nucleon at about 2.34 GeV/c2 . The Λ(1405) is considered−as the first excited state of Λ particle with J P = 21 in a quark model. Above the two
thresholds at 2.37 GeV/c2 , we also have a new type of threshold of K̄N N . In the K̄N N
system, a bound state which is called as a K − pp bound state is theoretically predicted
to exist as the J P = 0− , isospin I = 1/2 and total charge +1 because of the strong
attraction of the K̄N interaction in I = 0 [1]. The K̄N N system sits on above about
49 MeV and 27 MeV from the Σ(1385)N and Λ(1405)N systems, respectively. Thesesituations make it diﬃcult to theoretically study the K − pp bound state. On the other
hand, a πΛN –πΣN dibaryon, which is the bound state of the decuplet and octet baryons,is theoretically predicted in the Σ(1385)N system with I = 3/2 and J P = 2+ [2]. Thereis also a theoretical prediction of a bound state of the Λ(1405)N system [3]. Its quantum
number is I = 1/2 and J P = 0− . We can not distinguish the Λ(1405)N from theK − pp bound state when we consider the Λ(1405) is the bound state of the K̄N system.
It is no wonder that these three bound states would appear in anyplace between the ΣNand Σ(1385)N thresholds. Of course, the bound states are unstable; they decay into
light systems such as ΛN , ΣN , πΛN , and πΣN . In this thesis, we aim to investigate thestates in the strangeness S = −1 and baryon number B = 2 system around this energy
region. It is expected that strangeness degree of freedom plays an important role in highdensity nuclear matter realized in core of neutron star. For example, Λ hypereon might
appear at around twice the normal nuclear matter density. Beyond that density, thesystem we are investigating can take an important role. Therefore, it is an important
subject to understand the whole energy spectrum of strange dibaryon systems.

1.1

K̄N interaction

Information on the K̄N interaction was obtained from K − p scattering data in low-energy
region. In particular, Martin estimated the scattering length by using the self-consistent
M -matrix description for the low energy K̄N data of K − p → K − p (elastic), K − p → K̄N(charge exchange), and K − p → Λπ 0 , Σ0 π 0 , Σ± π ∓ (inelastic) with the K ± p and K ± n
dispersion relation as shown in Figure 1.2 [5]. The estimated scattering lengths1 at theK − p threshold are
aI=0 = −1.70 + i0.65 fm,
aI=1 = 0.37 + i0.60 fm,(1.1)

where aI=0 and aI=1 are the scattering lenghts with I = 0 and I = 1, respectively.
The information of K̄N is also obtained from the measurement of the Kα X-ray(2p → 1s transition) of kaonic hydrogen. The energy level shift from the electromagnetice.m.
measured) and the width (Γ1s ) of the ground state give us− E1s
calculation (∆E1s = E1s
information of S-wave K̄N interaction. These values can be compared with the K − pscattering data. The scattering length can be deduced from the ∆E1s and Γ1s through1

In this definition, the scattering length is attractive for Re a > 0 and vice versa.

1.1. K̄N INTERACTION

3

Figure 1.2: The low energy K − p scattering data and the curves calculated from the
M -matrix parameters. This figure is taken from Ref. [5].

4

CHAPTER 1. INTRODUCTION

the Deser relation [6, 7] as:i∆E1s + Γ1s = 2α3 µ2 aK − p ,2
1 I=0
aK − p =(a+ aI=1 ),
2

(1.2)
(1.3)

where α is the fine structure constant and µ is the reduced mass of the K − p system.
The deduced scattering length from the kaonic hydrogen data was not consistent with
the Martin’s result until 1997. Especially, the sign of the real part was in disagreementwith each other, whose discrepancy was called as “ kaonic hydrogen puzzle”.
IHW
MM
CS

700

OURS

Γ (eV)

600

500

SIDDHARTA
400

300

200

KEK
DEAR

100
-400

-350

-300

-250

-200

-150

−∆ E (eV)Figure 1.3: The comparison of the ∆E1s ’s and Γ1s ’s of the kaonic hydrogen reported bythree groups (taken from Ref. [14]). The experimental data with errors are indicatedby the sides of the rectangles corresponding to the KEK-PS E228 [8], DEAR [9] andSIDDHARTA [10] experiment. The recent theoretical values are also shown with a black
plus symbol [11], a blue cross [12], a green solid triangle [13] and a red empty circle [14].

This “kaonic hydrogen puzzle” was solved by KEK-PS E228 (KpX) experiment in1997. They observed a clear Kα peak by using a gaseous hydrogen target in order toreduce the backgrounds [8]. Later, the DEAR collaboration also published the kaonichydrogen atom data [9], whose obtained value was not so far from the value of KEK-PS
E228 experiment. Recently, the SIDDHARTA group measured the kaonic hydrogen Xray in high precision by using the silicon drift detectors (SDDs), which had both goodenergy resolution of about 150 eV and good time resolution of about 1 µs [10]. These∆E1s ’s and Γ1s ’s are summarized in Figure 1.3. In this figure, the recently calculated
values using the coupled-channel approach based on the chiral eﬀective theory (chiralunitary model) with the interaction kernel up to NLO level are also shown [11, 12, 13, 14].
Furthermore, in these theoretical works, they discuss the extrapolation of K̄N amplitude
into sub-threshold energy region. Here, we show the result in Figure 1.4 of Ref. [11, 15].
These theoretical models well reproduce the experimental values (kaonic hydrogen data,
K − p cross sections, and branching ratios), although details of models and fitting schemes1.2. Λ(1405)

5

are diﬀerent. However, some deviations are seen in the subthreshold extrapolations asshown in Fig. 1.4. These uncertainties may be attributed to the diﬀerence of the model
setup [14, 15]. Therefore, the K̄N interaction in the sub-threshold region is not wellconstrained at present and a new experimental constraint is necessary.

Figure 1.4: The K − p → K − p forward scattering amplitude extrapolated to the subthreshold region taken from Ref. [15]. The constraints from the result of SIDDHARTA
experiment are indicated by the dots. The shaded bands represent theoretical uncertainties.

1.2

Λ(1405)In the constituent quark model, Λ(1405) is assigned as a negative parity excited three−quark baryon of u, d, and s-quarks with isospin I = 0, and spin parity J P = 12 .
The constituent quark model correctly predicted many of existing hadron masses of theground and excited states [16]. However, the quark model is diﬃcult to reproduce themass of Λ(1405). In Figure 1.5, it is compared between the measured masses and thepredictions of the quark model for the strangeness S = −1 negative parity baryons. Massof the negative parity baryons was reproduced well with the quark model except for the−Λ(1405) (Λ∗ 21 ). According to the model, the Λ(1405) is the spin-multiplet partner of−−−the Λ(1520), which is the J P = 23 state, and these 12 and 32 states should almost
degenerate in mass at about 1490 MeV as shown in Figure 1.5.
However, the observed mass of Λ(1405) is smaller by about 80 MeV than the theoretical prediction. The mass diﬀerence between Λ(1405) and Λ(1520) is too large toexplain it with the LS splitting between quarks. Moreover, the mass of Λ(1405) is lighter−
than N (1535), which is a nucleon excited state with the same spin and parity J P = 21 ,although Λ(1405) has a strange quark. Then, the Λ(1405) is considered not three quark
state. In meson-baryon picture, the Λ(1405) is interpreted as a K̄N quasi-bound statewith I = 0 embedded in the Σπ continuum, which was discussed in coupled-channelmeson-baryon scattering models [17]. This is in some sense reasonable, because the massof Λ(1405) is located just below the K̄N threshold and the K̄N interaction is strongly
attractive in the I = 0 channel.

6

CHAPTER 1. INTRODUCTION

Figure 1.5: Comparison between the measured masses and the predicted one from theconstituent quark model of the strangeness S = −1 negative parity baryons taken from
Ref. [16]. The shadow boxes show the measured masses and the black bars show thepredicted masses from this model.

Recently, the Λ(1405) is discussed by using the chiral unitary model [18]. In thisstudy, the Λ(1405) is composed of two poles located between K̄N and πΣ thresholds.
Both poles contribute the observed experimental invariant mass distribution. In the
recent result in the NLO scheme including the constraints of SIDDARTA measurement,+3
one pole is located at 1424 +7−23 − i26 −14 MeV with a dominant coupling to K̄N and the+19other pole is at 1381 +18−6 − i81 −8 MeV with a strong coupling to πΣ [11]. Moreover, it
is understood that the strong energy dependence of the scattering amplitude shown in
Figure 1.4 is induced from the existence of Λ(1405).
In the experimental side, the existence of Λ(1405) was confirmed from Bubblechamber experiments using a π − and K − beam at Brookhaven [19] and CERN [20],respectively. In the recent years, several results with high statistics using the magnetic
spectrometer were reported. The Σ0 π 0 line shape was reported for the p + p reaction
at a 3.65 GeV/c at the Cooler Synchrotron (COSY) [21]. The Σ± π ∓ line shapes were
measured in the p + p collisions at Gesellschaft für Schwerionenforschung (GSI) by the
HADES collaboration [22] and the photo-production at the Super Photon ring-8 GeV(SPring-8) by the LEPS collaboration [23, 24]. From the LEPS data [24], the diﬀerence
between the line shapes of Σ+ π − and Σ− π + was reported, although the exact contribution from the Λ(1405) was not clear. Moreover, both Σ± π ∓ and Σ0 π 0 line shapes in highstatistics were measured by using the photo-production reaction at Thomas Jeﬀerson
National Accelerator Facility (JLab) by the CLAS collaboration [25]. These observed
line shapes are not always consistent with each other and these inconsistencies might beoriginated from the structure of the Λ(1405).

1.3. K̄-NUCLEUS INTERACTION

1.3

7

K̄-nucleus interaction

An important tool to study the K̄-nucleus interaction in low-energy region is kaonicatoms, which are coulombic bound state of the K − and nucleus with influence of strong
interaction, obtained by the X-ray spectroscopy. Recently, high precision experiments
were carried out to measure the kaonic 4 He and 3 He by KEK-PS E570 [26] and SIDDHARTA [27] experiments. The simple tρ approach, where t is the free space zeroenergy t matrix and ρ is the nuclear density, is widely used to obtain the hadron-nucleus
interaction. In this approach, global fits were carried out for a large set of data using an
optical potential Vopt with the Klien-Gordon equation,[∆ − 2µ(B + Vopt + Vc ) + (Vc + B)2 ]Ψ = 0,

(1.4)

where Vc is the static Coulomb potential for the K̄ due to the finite charge distributionof the nucleus, µ is the reduced mass of K − -nucleus system and B = BK̄+iΓK̄ /2 (BK̄ andΓK̄ are the binding energy and the width, respectively). The simple tρ optical potential
is given by,(µ A − 1)2µVopt (r) = −4π 1 +b0 ρ(r),(1.5)
m A
where m is the mass of nucleon and ρ(r) is the nucleon density distribution normalized
to the mass number A. The b0 is the fitting parameter which is equal to the K̄-nucleon
isoscalar scattering length in the impulse approximation. The tρ best-fit potentials had
the real parts depth of about −80 MeV for a typical medium-weight to heavy nucleus [28].
Such a “shallow” potential was obtained from the chirally inspired approaches which
fit the low-energy K − p reaction data [29]. Much shallower potential was derived byadditionally requiring self-consistency in the construction of the optical potential [30, 31].
The generic tρ potential in Eq. 1.5 was greatly improved by adopting a density dependent (DD) potential, where the fixed b0 was replaced by b0 → b0 + B0 [ρ(r)/ρ0 ].
The parameters b0 , B0 and α ≥ 0 were determined from the fit. In this global fits, 65
level-shifts and widths of the K − atom data from 7 Li to 238 U were used as shown in Figure 1.6. The density dependent optical potentials turned to give the “deep” potential,
whose depth of the real parts was −(150–200) MeV. The tρ with the multiplicative function approach [32] and the model independent Fourier-Bessel method [33] also provided
such a “deep” potential.
Recently, a K̄ nuclear potential study was carried out by using the Ikeda-HyodoWeise (IHW) NLO chiral K − N subthreshold scattering amplitude [11] as shown in Fig(1)ure 1.4 [34]. In this study, the single-nucleon density-dependent potential VK − (ρ) was
generated using the IHW amplitudes and a phenomenological density-dependent inter(2)action potential VK − (ρ) was added to reproduce multi-nucleon dispersive and absorptive(1)(2)
processes. Both VK − (ρ) and VK − (ρ) are coupled implicitly within a self-consistent cycle(1)(2)
built into the kaonic atom fitting procedure. Finally, the IHW-based (VK − (ρ) + VK − (ρ))
potential produced the deeply attractive real potential, whose depth at the center of Ni
was −191 MeV [34].
The other tool to investigate the K̄-nucleus interaction is the excitation spectrum in
the in-flight (K − , N ) reaction with nuclear targets. In KEK-PS E548 experiment [37],they measured the energy spectra both of the 12 C(K − , n) and 12 C(K − , p) reactions

8

CHAPTER 1. INTRODUCTION

Figure 1.6: The level-shifts (a) and widths (b) of the K − atom with the best-fit density
dependent optical potentials taken from Ref. [28].

Figure 1.7: Comparison between the DWIA calculation of the 1sΛ hypernuclear formation
rates in stopped K − reaction on several p-shell targets and measured values from the
FINUDA Collaboration [35]. This plots were normalized to the 1sΛ formation rate of the7Λ Li. Taken from Ref. [36].

1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

9and the potential depths were obtained as −190 MeV for the 12 C(K − , n) reaction and−160 MeV for the 12 C(K − , p) reaction with the Greens function method. However,there is a paper to point out a serious drawback in this experimental setup [38]. In
KEK-PS E548 experiment, at least one charged particle detected in their decay counter
was required. The paper pointed out that this requirement can appreciably distort the
spectrum shape.
Recently, the distinction between “deep” and “shallow” K − -nucleus potentials was
discussed by comparing the calculated 1sΛ hypernuclear formation rates in stopped K −reaction on several p-shell targets with measured values from the FINUDA Collaboration as shown in Figure 1.7 [36]. This comparison favors deep potentials to shallow
ones. However, it is not conclusive whether K̄-nucleus interaction potential is “deep” or“shallow” in the current situation. The study of the kaonic nuclei, which is the boundstates of kaon and nucleus, will help to solve this problem because the binding energies
and the width of each kaonic nucleus should depend on the potential depth and have theinformation of inner behavior of the strong interaction potential.

1.4

Kaonic nuclei: Experiments and Theory

The kaonic nuclei in medium-weight nucleus system was discussed by Kishimoto in1999 [39]. Akaishi and Yamazaki predicted the possible existence of the deeply boundkaonic nuclei for few body systems in 2002 [1]. From these period, a study of the kaonic
nuclei have been actively conducted from both theoretical and experimental sides. The
kaonic nuclei should have the rich information such as the K̄N strong interaction in
sub-threshold region, the strong interaction potential of the K̄ nucleus system and the
behavior of the Λ(1405) in many body systems.
In the Akaishi and Yamazaki’s theoretical work [1], they constructed a phenomenological K̄N interaction model using the K̄N scattering data, kaonic hydrogen data of the
KEK-PS E228 (KpX) experiment and the binding energy and width of the Λ(1405) byassuming the Λ(1405) as isospin I = 0 bound state of the K̄N system. They predicted
the kaonic nuclei with narrow widths of the K − +3 He, K − +4 He, and K − +8 Be systems
with binding energies of 108, 86, and 113 MeV and narrow widths of 20, 34, and 38 MeV,
respectively. In the paper [1], they also proposed an experimental method to populate−, n) reaction. Moreover, in Ref. [40], they discussed
the K − +3 He by using the 4 He(Kstopped
the kaonic nuclei in proton-rich system. The K − with two protons system, namely theK − pp bound state, was calculated with the binding energy of 48 MeV and the width of
61 MeV using their formalism. In this discussion [40], they proposed the (K − , π − ) and(π + , K + ) reactions to produce the proton-rich kaonic nuclei, where Λ(1405) and Λ(1520)
might play important roles as door-ways. This prediction inspires the present work.
After the Akaishi and Yamazaki’s prediction, several experiments to search the kaonic
nuclei were carried out. In KEK-PS E549 experiment [41, 42], they measured the missing−−, n) reactions to search for the K − ppn, p) and 4 He(Kstopped
mass spectra of the 4 He(Kstopped
and K − pnn bound states. However, no peak structures were observed in both spectra
as shown in Figure 1.8. The upper limits for the formation branch were obtained to bea few %/(stopped K − ).

10

CHAPTER 1. INTRODUCTION
(a)

(b)

−
−
Figure 1.8: The missing mass spectra of the 4 He(Kstopped, p) (a) and 4 He(Kstopped, n) (b)reactions obtained by KEK E549 experiment. Taken from Ref. [41, 42].

1.4.1

Past experiments of the K − pp

FINUDA experiment
The first evidence of the K − pp was reported by the Fisica Nucleare a DAΦNE (FINUDA) Collaboration [43] at DAΦNE, which is the e+ e− collider at the Laboratori Naziali
di Frascati (LNF) and produces copious ϕ(1020) mesons. In this experiment, almost
monochromatic K − ’s produced from the decay of ϕ(1020) mesons were stopped in fivekinds of thin targets (6 Li, 7 Li, 12 C, 27 Al, and 51 V). They measured a lot of Λp pairs
emitted in the opposite direction (cos θLab < −0.8) from the light nuclear targets (6 Li,
7Li, and 12 C). They observed a bump structure in the invariant mass spectrum of the Λppairs as shown in Figure 1.9. The obtained binding energy and the width, which were
estimated by fitting with a Lorentzian function folded with a Gaussian with the experi+3
mental invariant mass resolution σ = 4 MeV, were BK − pp = 115 +6−5 (stat.) −4 (syst.) MeV+2and ΓK − pp = 67 +14−11 (stat.) −3 (syst.) MeV, respectively. This experiment is the first experiment to detect the K − pp → Λp mode. Since the obtained width was large, to measure the invariant-mass spectrum leads to prosperity. After the FINUDA experiment,
K − pp → Λp mode is mainly used to search for the K − pp bound state.
In this analysis, there was a theoretical criticism that the obtained invariant mass
spectrum can be explained without K − pp [44]. They point out that a final state interaction of proton and Λ after the quasi-free two nucleon absorption can also produce thesimilar invariant mass distribution of FINUDA experiment. However, for their criticism,
there is also counterargument that the bump structure around this region was observed

1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

11

in the Λp spectrum but not in the Λn spectrum and the large diﬀerence between the Λpand Λn spectra is diﬃcult to explain with the final state interactions [45]. Therefore,
the interpretation of the observed spectrum of the FINUDA experiment seems to be notconclusive at present.
-BK-pp [MeV]
30

-250

-200

-150

-100

-50

0

25
2

counts/(10MeV/c )0arbitrary unit

-150 -100 -50

20
15

2.2 2.25 2.3 2.35 2.4

10
5
0
2.1

2.15

2.2

2.25

2.3

2.35

2.4

2

2.45

2.5

p-Λ invariant mass [GeV/c ]Figure 1.9: The Λp invariant mass spectrum obtained from the FINUDA experiment(taken from Ref. [43]).

DISTO experiment
After the report of FINUDA experiment, a possible signal of the K − pp was discussed
by the DISTO experiment [46], which was carried out at the SATURNE accelerator at
Saclay. They used the pp → K + pΛ reaction at Tp = 2.85 GeV and measured both
K + missing mass and Λp invariant mass. Deviation spectra were obtained from themeasured experimental spectra, which was not corrected experimental acceptance, divided by simulated phase space spectra of the pΛK + process taking into account of theacceptance.
A large broad peak in the deviation spectrum of missing-mass spectrum of K +was observed by applying cut of the large proton angle (| cos θcm (p)| < 0.6) and largeangle of K + emission (−0.2 < cos θcm (K + ) < 0.4) as shown in Figure. 1.10. The
obtained mass and width were M = 2267 ± 3 (stat.) ± 5 (syst.) MeV/c2 andΓ = 118 ± 8 (stat.) ± 10 (syst.) MeV, respectively, with the statistical significance of 26σ.
The obtained mass corresponds to a binding energy of 103 ± 3 (stat.) ± 5 (syst.) MeV
for the K − pp. The production rate of this broad peak was found to be as much as theΛ(1405) production rate, which is roughly 20% of the total Λ production rate. They also
analyzed the same reaction data at Tp = 2.5 GeV [47]. However, they did not observe
such a signal at this beam energy; may be due to the small production cross section of
Λ(1405) at Tp = 2.5 GeV.

12

CHAPTER 1. INTRODUCTION
B (K pp) [MeV]
200

100

0

large-angle proton: high-P T(p)2.5

M(K+p+p) = 2370

2.0

1.5
Γ = 118 (8)
1.0

0.5

0

2150

2200

2250

M(Λ*+p) = 2345M(Σ+π+p) = 2267

Deviation UNC/SIM (arb. scale)M = 2267 (2)2300

Missing Mass ΔM(K)

2350

2400

2450

[MeV/c 2 ]Figure 1.10: The deviation spectrum (DEV) of the of missing-mass spectrum of K +constructed from the DISTO experiment (taken from Ref. [46]).

OBELIX experiment
The OBELIX experiment [48, 49] was carried out at the LEAR complex at CERN using
the p̄ annihilation reaction on 4 He target. Especially, they discussed the p̄ +4 He →pπ − pπ + π − nX reaction, which corresponds to the p̄ +4 He → [K − pp]Ks0 nX → ΛpKs0 nX
reaction. In Ref. [48], they observed a peak with the statistical significance of 3.7σ
at the mass of 2212.1 ± 4.9 MeV, which corresponding to the K − pp binding energy of
160.9 ± 4.9 MeV, and width of < 24.4 ± 8.0 MeV in the (ppπ − ) invariant-mass spectrum
by selecting the events with the pπ − invariant mass close to the Λ mass (1115 ± 30 MeV),
although they did not observe clear Λ peak directly in the pπ − invariant-mass spectra
due to the poor resolution.
In Ref. [49], they reported the results which was improved the signal/background bychanging the analysis method. The main diﬀerence was in the selection of Λ. In thisanalysis, the Λ produced event was selected by checking not only the invariant mass ofpπ − but also the scatter plot of ptot and Etot , which corresponded to the momentum andenergy of the Λp system respectively, characterized by missing K 0 . Figure 1.11 shows theobtained (ppπ − ) invariant-mass spectrum with several cuts to achieve the best statisticalsignificance of 4.7σ by fitting with two Gaussian functions. The obtained peak position
and width were 2223.2 ± 3.2 (stat.) ± 1.2 (syst.) MeV, which corresponds to the K − ppbinding energy of −151.0 ± 3.2 (stat.) ± 1.2 (syst.) MeV, and < 33.9 ± 6.2 MeV,
respectively. (On the other hand, the obtained peak of the OBELIX experiment might
be attributed to a threshold cusp eﬀect at the Λpπ system [50].)

1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

13

Figure 1.11: The (ppπ − ) invariant-mass spectrum corresponding to the Λp state obtained
from the OBELIX experiment (taken from Ref. [49]).

LEPS experiment
The K − pp was also searched by using the photo-production at the LEPS/SPring-8 [51].
In this experiment, they used the d(γ, K + π − ) reaction at Eγ = 1.5–2.4 GeV and totally
7.6 × 1012 tagged photons were irradiated on a liquid deuterium target. The beamenergy Eγ was measured for each event with a tagging counter, whose energy resolution
was approximately 12 MeV, and the K + and π − which were produced in the forwardlab+ −angle (cos θK+ , π − > 0.95) were detected with the LEPS spectrometer. The d(γ, K π )reaction can be regarded as the virtual d(K − , π − ) or d(K ∗− , π − ) reactions when t-channel
reaction modes are dominant.
A peak of the K − pp was searched by using the Log-likelihood ratio method by assuming the background process as γn → ΛK + π − , γp → Σ+ K + π − , γp → Λ(1520)K + ,γn → Λπ 0 K + π − , γn → Σ0 π 0 K + π − and γp → Σ(1385)0 K + π − , whose yields were taken
into account as free parameters. The obtained spectrum could be fitted with only thesebackground processes and no peak structure was observed from 2.22 to 2.36 GeV/c2 asshown in Figure 1.12. The upper limits of the diﬀerential cross section of the K − pp wasdetermined to be 0.17–0.55, 0.55–1.7 and 1.1–2.9 µb at 95% confidence level with theassumed width of Γ = 20, 60 and 100 MeV, respectively.
Furthermore, in order to investigate the background precisely, they fitted missingmass spectra of d(γ, K + π − ) and d(γ, K + ) reactions assuming the proton mass for thetarget mass simultaneously by supposing the total 12 quasi-free processes. In the fit
result, they found that the main contribution to the missing-mass spectrum in the K − pp
search region was originated from the γp → Λ(1520)K + process (22 ± 3%) and nonresonant hyperon production processes of γN → Λ/ΣπK + π − (24 ± 5%).

14

CHAPTER 1. INTRODUCTION

Figure 1.12: The d(γ, K + π − ) missing-mass spectrum of the LEPS experiment (takenfrom Ref. [51]).

HADES experiment
The HADES Collaboration at GSI also searched for the K − pp by using the pp → pΛK +reaction at Tp = 3.5 GeV [52, 53], whose beam energy was higher than the one of the
DISTO experiment. In Ref. [52], they compared the obtained invariant mass of ΛK + ,pK + and Λp system and angular distribution spectra with the simulated one calculatedwith a pure phase-space event generator. They found that the phase-space simulation
could not reproduce the obtained invariant mass and angular distributions. The disagreement could not be overcome by adding the contribution of (one) resonances. Furthermore, since the obtained K + Λ invariant mass spectrum showed two peaks around 1700
and 1900 MeV/c2 , they added incoherently the phase space production to the N(1720)
and N(1900) contributions. Then, they achieved a better description of the experimental
data. Moreover, they built the deviation spectra (DEV) by dividing the experimental
data with the simulation including the N ∗ contribution, although the DISTO experimentassumed the pure-phase space distribution. The deviation spectrum of the Λp invariant
mass showed a wide bump around 2400 MeV/c2 . They pointed out that the obtained
bump at the deviation spectrum of the HADES experiment jeopardized the solidity ofthe deviation method used by the DISTO collaboration.
Recently, they reported the result employing the Bonn-Gatchina partial wave analysis
framework (PWA) in Ref. [53]. In the PWA, they used ten versions of the non-resonant
production waves and twelve versions of N ∗ resonances as the PWA inputs. They fitted
the data with their combination of 120 diﬀerent ansatzes. The four best PWA solutions
were obtained with a null hypothesis of the existence of the K − pp which decayed toΛp mode. Figure 1.13 shows the comparison between the obtained (black dotes) and
the PWA solutions (gray band), whose error band shows the systematic diﬀerences ofthe four best PWA solutions, of the (ΛK + , pK + , Λp) invariant mass spectra which are1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

15

one of the spectra used for the fitting. Finally, they evaluated the upper limits on theK − pp in the mass range of 2220–2370 MeV/c2 and assuming the widths of 30, 50 and
70 MeV for the three possible production waves of J P =0+ , 1− , 2+ , where the quantum
numbers of the K − pp was assumed as J P = 0− . The evaluated upper limits of theK − pp decaying to Λp mode were 1.8–3.9 µb (J P = 0+ ), 2.1–4.2 µb (J P = 1− ) and
0.7–2.1 µb (J P = 2+ ). Moreover, the obtained upper limits about 4 µb was discussed
by comparing the measured production cross section of the Λ(1405) of about 10 µb from
evaluated from the same experiment [22].

Figure 1.13: The obtained (ΛK + , pK + , pΛ) invariant-mass spectra with the solution of
PWA evaluated from HADES experiment (taken from Ref. [53]).

J-PARC E15 experiment
In the E15 experiment, they have used the in-flight 3 He(K − , n) reaction at 1 GeV/c [54].
They measured not only the missing-mass spectrum of the 3 He(K − , n) reaction but also
an invariant-mass spectrum of the decay particles such as Λp pairs. The outgoing neutron
at θnlab = 0◦ was measured by the time-of-flight method using a neutron counter hodoscope
placed at a distance of about 15 m from the liquid 3 He target. The decay particles weredetected by using the Cylindrical Detector System (CDS), which surrounded the target.
The first physics run of this experiment was carried out in May 2013. In this datataking, they irradiated 5.3 × 109 kaons, which corresponds to about 1% of statistics
requested in the original proposal. In Ref. [54], a result of the 3 He(K − , n) missingmass distribution based on a semi-inclusive condition by requesting at least one charged
track in the CDS was discussed. Figure 1.14 shows the reported 3 He(K − , n) semiinclusive missing-mass distribution together with the estimated backgrounds for theK − pp bound region. They confirmed the observed events in the missing-mass region
below 2.29 GeV/c2 were explained by the background such as a neutron event from theΣ± decay. On the other hand, they pointed out that the yield of the tail like component
above 2.29 GeV/c2 cannot be totally reproduced. It might originate from the imaginary part of the attractive K̄N interaction and/or hyperon resonance production via thenon-mesonic two-nucleon absorption processes. They evaluated the upper limits of the
production cross section of the K − pp assuming the isotropic decay of the K − pp → Λp at

16

CHAPTER 1. INTRODUCTION

95% confidence level in the missing-mass range from 2.06 to 2.29 GeV/c2 . The obtained
upper limits were 30–180, 70–250, and 100–270 µb/sr, for the widths of 20, 60, and
100 MeV, respectively. The analysis using the CDS for the decay particles are on going.
(This analysis result will be also reported in near future.)

0.15

0.1

0.05

M(Σ+N+π)M(Σ+N)14

M(Λ +N+π)

18
16

0
350
300

2

0.2

250

12
200

10

Data
BGΣ -decay
BGcell
BGaccidental+neutral

8
6
4

150
100
50

2
0
2

Counts / 10 MeV/c

0.25

M(Λ (1405)+p)

20

0.3

M(Λ +p)d2σ/dΩ/dM × ACDS (μb/sr/(MeV/c2))

Binding Energy [GeV]
0.35

2.05
3

2.1
-

2.15

2.2

2.25

2.3

2

2.35

0

He(K ,n)X missing mass (GeV/c )Figure 1.14: The semi-inclusive 3 He(K − , n) missing mass spectrum with estimated backgrounds of the J-PARC E15 experiment (taken from Ref. [54]).

1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

1.4.2

17

Current situation of the K − pp

FINUDA, DISTO and OBELIX experiments observed the peak structure which can be
attributed to the signal of the K − pp. However, the obtained experimental values are
not consistent with each other. There are no experimental evidence which can conclude
the existence of the K − pp. In the FINUDA experiment [43], there is a theoreticalcriticism that the final state interaction of proton and Λ after the quasi-free two nucleon
absorption can produce the similar bump structure [44]. Since they used nuclear targets
such as 12 C, the contribution of the final state interaction could be larger. In orderto reduce the final state interaction eﬀect, it is better to use the lighter targets. Notethat there is further experiment to search for the K − pp using the stopped K − reaction
at DAΦNE (AMADEUS experiment [55]) using 4 He target to reduce the final stateinteraction eﬀect. Furthermore, the reaction mechanism to produce the K − pp from thestopped K − reaction was not investigated. In this view, OBELIX experiment [48, 49] also
has the same problem in the p̄ annihilation reaction. In addition, they did not observe
clear Λ peak directly in the pπ − invariant-mass spectra due to the poor resolution.
Moreover, the peak structure measured by OBELIX experiment might be the thresholdcusp of the Λpπ system [50].
The DISTO experiment introduced the deviation spectra which were made from themeasured spectra divided by simulated spectra [46]. They assumed the phase spacepΛK + production reaction in the simulation as for the background reaction. However,it seems there is an ambiguity of the background assumption because they used the
pp → K + pΛ reaction at Tp = 2.85 GeV. In this reaction, there should be additional
background processes such as N ∗ production, which is pointed out by the HADES collaboration [52, 53]. The HADES collaboration, which also used the pp → K + pΛ reaction
at Tp = 3.5 GeV, performed the partial wave analysis (PWA) using the components of
non-resonant production waves and N ∗ resonances in order to understand this reaction.
They found the four best PWA solutions without the hypothesis of the K − pp when they
fitted with 120 diﬀerent ansatzs. Thus, there are a lot of background reactions in the pp
reaction at these energy region. By using the pp reaction, FOPI experiment also searches
the K − pp at Tp = 3.1 GeV at GSI [56].
The LEPS collaboration evaluated the upper limit using the inclusive spectrum inthe d(γ, K + π − ) reaction [51] . Since they used the inclusive spectrum, there were a lotof background processes of the hyperon and hyperon resonance productions. Thus, theinclusive measurement seems less sensitive to search for the K − pp. Note that they are
considering a further experiment for the K − pp search with the exclusive measurementin the γd → K + π − Λp reaction at LEPS2 [64].
In the J-PARC E15 experiment [54], they used 3 He(K − , n) reaction to search for theK − pp. They supposed the K − pp is expected to be produced directly from a 3 He nucleus
in this reaction. However, we do not know whether this reaction model is valid or not.
In order to clarify the reaction mechanism, it is important to investigate an elementarycross section of the Λ(1405) production. They measured missing-mass spectrum of the3
He(K − , n) reaction and invariant-mass spectrum of decay particles such as Λp pairs.
In the semi-inclusive analysis, they evaluated the upper limits for the K − pp productionin the missing-mass range from 2.06 to 2.29 GeV/c2 . The analysis constructing theinvariant mass spectrum of the Λp pairs by requiring the final state to be Λpn, whose

18

CHAPTER 1. INTRODUCTION

spectrum is expected to have less background, is on going.
In order to investigate whether the K − pp exists or not, we should know the reaction
mechanism to produce the K − pp. Moreover, it is important to investigate the K − pp byusing the diﬀerent reactions in order to reduce the other possibility such as a final stateinteraction. Here, it is better to use the lighter target to reduce the component of the
final state interaction. In addition, the background reactions should be controlled. In
this view, we proposed a new experiment to search for the K − pp using the d(π + , K + )reaction.

1.4. KAONIC NUCLEI: EXPERIMENTS AND THEORY

1.4.3

19

Theoretical studies of the K − pp

The K − pp has been also studied from the theoretical side using diﬀerent treatmentsof the K̄N interactions and a few-body calculation methods [40, 57, 58, 59, 60, 61,62]. For the K̄N interaction, usually two types of potentials are used, namely chiralSU(3)-based energy-dependent potentials and the energy-independent potentials, whose
potential is constructed with the phenomenological treatment. There are also two typesof the calculation methods: one is a variational method with eﬀective single-channel
potential and the other is Faddeev coupled-channel method.
The calculated binding energy and width of the K − pp was summarized in Ref. [63] (especially Table 1) characterized of the types of K̄N interaction and calculation method.
We plot these predicted binding energies and widths in Figure 1.15 together with theexperimental values reported from the FINUDA [43], DISTO [46] and OBELIX [49]experiments. In this plot, the values using the chiral SU(3)-based energy dependent
potentials are shown with circles and the ones calculated with the energy independent
potentials are indicated with triangles. Moreover, the values obtained using the calculation method of the variational and the Faddeev approach are shown in black and whitecolors, respectively. The experimental values are indicated with red squares.

140

DISTO

ΓK - pp [MeV]120

N.V.Shevchenko, A.Gal, J.Mares

100
Y.Ikeda, T.Sato

80A. Dote, T.Hyodo, W.Weise

T.Yamazaki, Y.Akaishi

60

FINUDA
N.Barnea, A.Gal, E.Z.Liverts

40

OBELIX

S.Wycech, A.M.Green
Y.Ikeda, H.Kamano, T.Sato

20
0

0

20

40

60

80

100 120 140
BK - pp [MeV]

Figure 1.15: Summary of the calculated binding energy and width, which were listed inRef. [63], together with the experimental values of the FINUDA [43], DISTO [46] andOBELIX [49] data. For the experimental values, the statistical and systematic errors areshown with the blue and green lines, respectively. See the text for the detail.

Although all of the theoretical predictions listed in Ref. [63] agrees in the existenceof the K − pp bound state, the predicted binding energy and the width are not consistent with each other. Especially, the calculated binding energy using the chiral energy
dependent potentials (shown in circles) seems to be lower than the values of the energy
independent potentials (shown in triangles). It is discussed that this tendency appears
because of the diﬀerence between the (K̄N )I=0 interaction strengths which yield a quasibound state at about 1420 MeV in the former case and at about 1405 MeV in the latter

20

CHAPTER 1. INTRODUCTION

case [63]. Note that theoretical calculations of the K − pp are diﬃcult to reproduce themeasured binding energy about 100 MeV.
In the other view of the S = −1 and B = 2 system, the πΛN –πΣN dibaryon,
which can be a quasi-bound state of Σ(1385)N and ∆(1232)Y component, is discussed
theoretically [2]. A quantum number of this state is isosipin I = 3/2 and spin parity
J P = 2+ . The mass is predicted to be about 2.27 GeV/c2 which is 50 MeV below theΣ(1385)N threshold. Moreover, the Λ(1405)N bound state is also discussed [3]. In thisstudy, they found the quasi-bound state slightly below the Λ(1405)N threshold in the
total spin 0 channel.

1.5

J-PARC E27 experiment

The J-PARC E27 experiment was proposed to investigate the K − pp bound state byusing the (π + , K + ) reaction on a liquid deuterium target at 1.69 GeV/c. In this reaction, a production mechanism for the K − pp was discussed in Ref. [69]; a hyperon
resonance Λ(1405) is produced in the π + “n”→ K + Λ(1405) process as a doorway to theK − pp formation through Λ(1405)“p”→ K − pp. Here, “n” and “p” indicate a neutron
and a proton in a deuteron, respectively. It should be noted that an elementary crosssection of the π + “n”→ K + Λ(1405) reaction can be estimated from the cross section ofthe π − p → K 0 Λ(1405) reaction assuming the isospin symmetry. The elementary crosssection of Λ(1405) has already been measured by using the hydrogen bubble chamber at
pπ− = 1.69 GeV/c [19]. Figure 1.16 (a) shows the Σ± π ∓ invariant-mass spectrum obtained in this old experiment [19]. The Λ(1405) mass distribution was clearly observed inthis spectrum. Moreover, the angular distribution of Λ(1405) production was also measured as shown in Figure 1.16 (b). We can find the elementary Λ(1405) production crosssection is large at the very forward scattering angle. Thus, in the E27 experiment, wemeasured the (π + , K + ) reaction in the forward scattering-angle, where a lot of Λ(1405)’s
were produced. We have an advantage to be able to compare the K − pp cross section
with the elementary production cross section of the Λ(1405). It is a unique advantage
compared with any other experiments.
In addition, we can control the background process. In the d(π + , K + ) reaction, possible main background components are hyperons and hyperon resonances productionin quasi-free processes of π + “N ”→ K + Y (Y ∗ ) reaction, where “N ” is a nucleon in the
deuteron. The elementary cross sections of the π + p reactions have already been measured
in the old bubble chamber experiment [65]. In case of the π + n elementary cross sections,
we can estimate the ones from the π − p → K 0 Y (Y ∗ ) reaction as same as the Λ(1405).
These π − p cross sections were also measured by using a bubble chamber [19]. Thus,
we can reliably estimate these quasi-free background processes by using the measured
elementary cross sections. Moreover, the kinematics, especially the proton kinematics,
between the quasi-free backgrounds and the K − pp is diﬀerent. A proton can be produced
from the decay of hyperon such as Λ → pπ − in the quasi-free hyperon production (background). Such a proton’s scattering angle in the quasi-free processes concentrates in theforward angle (θp(Lab) ≲ 30◦ ) according to our simulation. On the other hand, a proton
produced from the K − pp decay such as K − pp → Λ(Σ0 )p process can distribute in a wide
scattering-angle region. Therefore, we can reduce the quasi-free background components

1.6. THESIS COMPOSITION

21

(a)
(b)

Figure 1.16: The Σ± π ∓ invariant mass spectrum (a) and the angular distribution (b)of Λ(1405) measured by the old hydrogen bubble chamber experiment. Taken from
Ref. [19].

by tagging the large scattering-angle (θp(Lab) ≳ 30◦ ) proton. Note that we can detect theK − pp signal free from the quasi-free backgrounds by measuring the two-protons in the
scattering angles θp(Lab) ≳ 30◦ . Furthermore, we can eliminate the final state interaction
for the K − pp because we use the liquid deuterium target.
This experiment was carried out at K1.8 beam line [66, 67] of the hadron experimental hall at J-PARC [68] in 2012. We reconstructed the missing mass by measuring theincident beam π + momentum with the K1.8 beam line spectrometer and the emitted K +momentum with the superconducting Kaon Spectrometer (SKS). The SKS has a good
momentum resolution about 0.2% (FWHM) and wide acceptance about 100 msr. Therefore, we can measure the missing mass spectrum of d(π + , K + ) reaction with the good
missing-mass resolution of about 3 MeV (FWHM) and the wide missing-mass region fromquasi-free Λ production region (∼2.05 GeV/c2 ) to Y ∗ production region (∼2.5 GeV/c2 ).
This experiment can overcome all the problems which hampered other experiments. It
is because we know the reaction mechanism to produce the K − pp and the elementarycross section of the Λ(1405). Moreover, we can control the background processes andeliminate the final state interaction for the K − pp.

1.6

Thesis composition

This thesis is arranged by the following order. The J-PARC E27 experiment and theexperimental setup are described in Chapter. 2. The detail of the inclusive analysis ofthe (π + , K + ) reaction is described in Chapter. 3. The coincidence analysis by using therange counter array (RCA) to detect the proton(s) is shown in Chapter. 4. The results ofboth inclusive and coincidence analyses are shown in Chapter. 5. We also discuss physics
interpretations for the obtained results. Finally, the conclusion is given in Chapter. 6.

Chapter 2
Experiment
2.1

Outline

The J-PARC E27 experiment was carried out at the K1.8 beam line of the J-PARC
hadron experimental hall in 2012. The goal of this experiment is to search for theK − pp bound state by using the (π + , K + ) reaction on a liquid deuterium target at pπ+ =1.69 GeV/c. A typical beam intensity was 3 × 106 per 6-second per spill cycle with aspill length of about 2 seconds.
In order to measure the momenta of beam pion and emitted kaon, the K1.8 beamline spectrometer and the superconducting Kaon Spectrometer (SKS) were used, respectively. Furthermore, a range counter array (RCA) was installed surrounding theliquid deuterium target in order to suppress a large backgrounds coming from quasi-free
productions of hyperon (Λ and Σ’s) and hyperon resonances (Λ(1405) and Σ(1385)’s).
In Chap.2.2, J-PARC accelerator facility and hadron experimental facility are described. In Chap.2.3, the detail of K1.8 beam line is described. The details of theK1.8 beam line spectrometer, SKS, the liquid target and RCA are shown in Chap.2.4,
Chap.2.5, Chap.2.6 and Chap.2.7, respectively.

2.2

J-PARC and hadron experimental facility

The Japan Proton Accelerator Research Complex (J-PARC) (Figure 2.1) is a multipurpose proton accelerator facility which aims to pursue frontier in nuclear physics,
particle physics, materials and life sciences and nuclear technology using MW-class,proton beams in these proton energies; 400 MeV, 3 GeV and 30 GeV [68]. The J-PARC
consists of three accelerators (a linac, a 3 GeV rapid-cycle synchrotron: RCS, and themain ring: MR) and three experimental facilities (a materials and life science facility:
MLF, a neutrino facility: NU, and a hadron experimental facility: HD).
The linac is composed of an H− ion source (IS), a radio frequency quadrupole (RFQ),
a drift tube linac (DTL) and a separated-type DTL (SDTL) [70]. H− was produced at
the IS and accelerated up to 181 MeV with a peak current 30 mA as of 2012. The beamenergy of the linac was upgraded to 400 MeV in 2013.
The H− beam from the linac was delivered to the RCS and converted to proton (H+ )by using a carbon stripper foil [71]. The RCS accelerates the injected proton up to22

2.2. J-PARC AND HADRON EXPERIMENTAL FACILITY

23

Figure 2.1: Schematic view of J-PARC (taken from Ref. [68]).

3 GeV. The 3 GeV beam from the RCS is mainly transported to the MLF and a part of
the RCS beam is transported to the MR [72]. The MR accelerates up to 30 GeV, anddelivers it to the NU by fast extraction and to the HD by slow extraction. The operationof the J-PARC accelerator was started in 2009.

Figure 2.2: Schematic view of hadron experimental facility (taken from Ref. [66]).

The primary proton beam from the main ring was extracted to HD for a duration of
2 seconds in every 6 seconds, which is synchronized to the J-PARC 30-GeV PS operation
cycle. The duration of the beam extraction is called a spill. The HD consists of a
primary beam line, three charged secondary beam lines (K1.8, K1.8BR and K1.1BR)

24

CHAPTER 2. EXPERIMENT

and one neutral secondary beam line (KL) as shown in Figure 2.2. The proton beam istransported from the MR to the HD and bombarded to the production target, T1 [73].
In the present experiment, the production target was a platinum rod (ϕ6 mm ×60mm). Secondary hadron beams such as kaon and pion produced at T1 were delivered toexperimental areas through the secondary beam lines [66].

2.3. K1.8 BEAM LINE

2.3

25

K1.8 beam line

Figure 2.3: Schematic view of K1.8 Beam line.

The K1.8 beam line is a general-purpose mass-separated beam line that can supply
secondary hadron beams of K ± , π ± , p and p̄ up to 2.0 GeV/c [66, 67]. It was designed fora spectroscopic study of Ξ hypernuclei and a systematic study of the double strangenesssystems by using the (K − , K + ) reaction by achieving the K − /(π − + µ− ) ratio of larger
than 1 at the kaon beam intensity of 10 MHz on an experimental target. In the present
experiment, we used the π + beam at 1.69 GeV/c with a typical beam intensity of 3 × 106
per spill, where it was limited due to a non-uniform time structure of the beam.
Figure 2.3 shows a schematic view of the K1.8 beam line. The K1.8 beam line iscomposed of 4 sections: the front-end section, the first mass separation section, thesecond mass separation section, and the beam analyzer section. The total length of thebeam line is about 46 m. The primary beam intensity on the production target was
typically of 7.5 × 1012 proton/spill for the present experiment.
Front-end section
Front-end section from D1 to IFV is shown in Figure 2.3. Two dipole magnets (D1 and
D2) and two quadruple magnets (Q1 and Q2) are installed. The extraction angle is chosen
to be 6◦ , where the kaon production cross section is expected to be at the maximum.

26

CHAPTER 2. EXPERIMENT

Some of the beam line elements in this section are operated in a large vacuum tank of∼1Pa.
The transported beam is vertically focused at the intermediate focus (IF) point.
Both horizontal and vertical beam profiles are shaped with a horizontal (IFH) slit anda vertical (IFV) slit. The so-called cloud pions which are produced by the decay of Ks0
and the scattered pions by materials of the upstream section are rejected by these slits.
This is one of the essential components in order to enhanced the purity of kaon. For the
IF slits, 30-cm thick brass blocks are used.
Mass separation section
The first mass separation section is from Q3 to D3 and the second mass separation
section is from Q7 to MS2 in Figure 2.3. The double-stage mass separation system isan essential component of the K1.8 beam line. In the mass separation section, a dipole
magnet (D3), seven quadruple magnets (Q3–Q9), four sextuple magnets (S1–S4), threeoctupole magnets (O1–O3) and two electrostatic separators (ESS1 and ESS2) with four
correction magnets (CM1–CM4) are located.
Two electrostatic separators are employed to separate kaons from pions in the firstand second mass separation sections. An electrostatic separator generates a transverse
electric field along the beam axis to separate particles of the same momentum by theirmass diﬀerences. Each electrostatic separator generates an electric field in the 10 cm gap
between parallel electrode plates with a size of 30 cm in width and 6 m in length. The
maximum gradient of the electric field is 750 kV/cm adding He(36.9%)/Ne insulating
gas in the chamber up to a few times 10−2 Pa. In this condition, the number ratio of
the kaon over other particles such as pion and muon in the beam is expected to be 3.5
at the beam momentum of 1.8 GeV/c. In the present experiment, ESS1 and ESS2 wereset at 200 kV/cm and 150 kV/cm, respectively.
The particle orbits are corrected by correction magnets (CM1–CM4) located both at
the entrance and the exit of the electrostatic separators. After ESS1 and ESS2, the beam
is focused in the vertical direction at each mass slit (MS1 and MS2). For the present
pion beam experiment, the setting of correction magnets were adjusted to let pions only
pass through the slit. A horizontal momentum slit (MOM) determines the momentum
bite of the secondary particles.
Beam analyzer section
Beam analyzer section which is called as K1.8 beam line spectrometer with a QQDQQ
magnet configuration is placed after the second mass slit, MS2. The beam is focused on
an experimental target and the beam momenta are analyzed particle by particle.
In the present experiment, the central beam momentum was set at 1.69 GeV/c for thed(π + , K + ) reaction and a typical momentum bite was about 1.6% (FWHM), as shownin Figure 2.4. Figure 2.5 shows typical beam profiles at the experimental target in thepresent experiment. A typical beam size was 7.6 mm (horizontal)×4.2 mm (vertical)
in σ. A liquid target, whose shape was cylindrical with 67.3 mm in diameter, fully
covered the incident beam. The derivatives of the horizontal (dx/dz) and vertical (dy/dz)

2.3. K1.8 BEAM LINE27

directions on the experimental target position were 0.01 rad and 0.004 rad in rms (rootmean-square), respectively. Here, in the coordination system, x, y and z coordinatescorrespond to the horizontal, vertical and beam directions, respectively.

28

CHAPTER 2. EXPERIMENT

9000
8000

Counts

7000
6000
5000
4000
3000
2000
1000
0
1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74

Beam momentum [GeV/c]

9000
8000
7000
6000
5000
4000
3000
2000
1000
0

16000

(a)

14000

(b)

12000
10000

CountsCountsFigure 2.4: Typical beam momentum distribution of π + in the present experiment.

8000
6000
4000
2000

-40 -30 -20 -10

0

10

20 30

0

40

-40 -30 -20 -10

Horizontal position (x) [mm]Counts

10000

25000

(c)

10

20 30

40

20000

(d)

Counts12000

0

Vertical position (y) [mm]

8000

15000

6000

10000

4000
5000

2000
0
-0.1

-0.05

0

0.05

0.1

Horizontal angle (dx/dz ) [rad]

0

-0.04

-0.02

0

0.02

0.04

Vertical angle ( dy/dz ) [rad]Figure 2.5: Typical beam profile at the experimental target in the E27 experiment measured by tracking chambers at the down stream of the K1.8 beam line spectrometer. The
horizontal and vertical positions are shown in (a) and (b), respectively. The derivativesof the horizontal (dx/dz) and vertical (dy/dz) directions are shown in (c) and (d).

2.4. K1.8 BEAM LINE SPECTROMETER

2.4

29

K1.8 beam line spectrometer

Overview

K1.8 beam line spectrometer

Target
BH2
BC4
BC3

5m

Q13
Q12
D4
GC BH1BC1 BC2Q10 Q11

Figure 2.6: Schematic view of K1.8 beam spectrometer.

The end-part of the K1.8 beam line is used as a beam spectrometer [75] to analyze
momentum and trajectory of each beam particle. Figure 2.6 shows a schematic viewof the K1.8 beam spectrometer. The K1.8 beam line spectrometer consisted of a gas
Čerenkov counter (GC), a timing plastic scintillation hodoscope (BH1 and BH2), two
MWPCs (BC1 and BC2), QQDQQ magnets and two drift chambers (BC3 and BC4).
Beam trajectories are measured by two sets of wire chambers at the entrance (BC1,2) and exit (BC3, 4) of the K1.8 beam line spectrometer for momentum analysis andreaction vertex reconstruction. For the momentum reconstruction, a third-order transfer
matrix was used through the QQDQQ system. A vacuum chamber and ducts are installedin the magnet region and the vacuum windows are made of 0.1 mm thick SUS. Point-topoint optics is realized between the entrance and exit of the QQDQQ system. Therefore,
the multiple scattering at the entrance and exit of the QQDQQ does not aﬀect the
momentum resolution to the first order. The design momentum resolution is 3.3 ×
10−4 (FWHM) with the position accuracy of 0.2 mm(rms) [75]. The magnetic field of
the dipole magnet (D4) was monitored during the experiment with a high-precision Hall
probe [Digital Teslameter 151 (DTM-151)] with the accuracy of 1.7 × 10−6 [76]. The

30

CHAPTER 2. EXPERIMENT

Table 2.1: Design specifications of the K1.8 beam line spectrometer
Momentum resolution
Maximum momentum
Bending angle
Flight path (BH1−BH2)
Eﬀective length (D4)

3.3×10−4 (FWHM)
2.0 GeV/c64◦
10.4 m4m

observed fluctuation ( ∆B
) was less than 0.05%. Design specifications of the K1.8 beamBline spectrometer are listed in Table 2.1.

Trigger counters
Three sets of trigger counters (GC, BH1, and BH2) are installed for particle identification. Specifications of the trigger counters of K1.8 beam line spectrometer are listed inTable 2.2.
Table 2.2: Specifications of the trigger counters of the K1.8 beam line spectrometer
Name
GC
BH1
BH2

Sensitive area
W×H×T (mm)340×80(mirror), 290L
170×66×5
145×60×5

Spec.
iso-C4 H10 , n∼1.002 (1.5 atm)
11 segments, 3-stage booster
7 segments, 3-stage booster

PMT(Hamamatsu)
R1250-03 (UV glass)H6524MOD
H6524MOD

Gas Čerenkov counter
Although the beam particles are selected by using the time-of-flight between BH1 and
BH2, electrons or positrons cannot be separated from pions over the beam momentumof 1 GeV/c. Thus, a gas Čerenkov counter (GC) is necessary for pion beam experiments
in order to reject electrons or positrons. It was installed at the most upstream of theK1.8 beam line spectrometer. Figure 2.7 shows a schematic view of GC. An isobutane
gas of 0.15 MPa was used as the radiator. The reflection mirror was a borosilicate glass
evaporated with aluminum. In order to protect aluminum from the oxidation, the surface
is coated with the manganese fluoride (MgF2 ) which is transmissive to the ultravioletlight region. In addition, the UV transparent window PMT was equipped in order toincrease the detection eﬃciency. The configuration of the mirror and the PMT was
optimized to focus the Čerenkov radiation on to the photo-cathode of the PMT.
The measured number of photo-electrons was approximately 5 for electrons of≥ 0.5 GeV/c. The eﬃciency of GC for electrons and positrons was found to be 99.5%. It
was enough to reject the electron (or positron) contamination of 12−14% in the beam.

2.4. K1.8 BEAM LINE SPECTROMETER

31

Hamamatsu
R1250-03 (UV glass)

200 mmyx

250 mmf340 mm

80 mm
Glass
t=6 mmMirror

290 mmAl
t=1 mmz

BeamAl
t=1 mmFigure 2.7: Schematic view of GC.

BH1 and BH2 counter
Beam particles were identified by the time-of-flight measurement between plastic scintillator hodoscopes of BH1 and BH2. BH1 and BH2 were installed upstream of BC1
and downstream of BC4, respectively. The flight length was 10.4 m, where the time
diﬀerence between kaons and pions is 1.3 ns at 1.69 GeV/c.
BH1 was segmented into 11 vertical pieces of 5 mm-thick plastic scintillators with
diﬀerent widths of 8, 12, 16 and 20 mm, as shown in Figure 2.8. The width of eachsegment was adjusted for the single counting rate to be uniform. Each segment was
overlapped with its adjacent segments by 1 mm to avoid a dead space and the eﬀective
area was 170 mm (horizontal) × 66 mm(vertical). H1650MOD phototubes equippedwith a three-stage booster, were connected on both ends of each scintillator.
BH2 was composed of 7-segment plastic scintillators with 5-mm thickness and different widths of 15, 20 and 30 mm, as shown in Figure 2.8. It defined the start timing
for all timing measurements. In the case of BH2, there were no overlapping in order
to avoid the position dependence of the energy losses caused by the overlappings. The
eﬀective area was 145 mm (horizontal) × 60 mm(vertical). The same phototubes as the
BH1 were connected on both ends of each scintillator.

Tracking wire chambers
Specifications of the tracking wire chambers in the K1.8 beam line spectrometer are
summarized in Table 2.3. MWPCs (BC1, 2) were placed at the entrance of the QQDQQ

32

CHAPTER 2. EXPERIMENT

Back

Front

Side

Y
A crylic
Light Guide

Beam
t=5

X
66

Scintillator
BC420

H amamatsu
H 6524MOD

Beam
12

20

170

8
8
16

30

Figure 2.8: Schematic view of BH1.

Back

Front

Side

Y
AcylicLight Guide

Beam

t=5

X
60

Scintillator
BC420

Hamamatsu
H 6524MOD

Beam
15

20

145

15
30

Figure 2.9: Schematic view of BH2.

2.4. K1.8 BEAM LINE SPECTROMETER

33

magnet system and drift chambers (BC3, 4) at the exit. The structure of the tracking
wire chambers are shown in Figure 2.10.
Table 2.3: Specifications of the MWPC (BC1, 2) and the drift chambers (BC3, 4) of theK1.8 beam line spectrometer

Name
BC1
BC2
BC3
BC4

Area
W×H (mm)
256×150
256×150
192×100
240×150

Anode pitch or
Drift length (mm)
1 mm pitch
1 mm pitch
1.5
2.5

Wires
xvuxvuvuxvuxxx′ vv ′ uu′
vv ′ uu′ xx′

Angle (x, u, v)(◦ )0, +15, −150, +15, −150, +15, −150, +15, −15

Resol. (expected)(µm in σ)
300
300
200
200

BC1, 2 (MWPC)
Tracking device should be operated under a very high counting rate of 10–20 MHz at
the entrance of K1.8 beam line spectrometer. In order to handle such a high counting
rate, MWPC with the anode pitch size of 1 mm and the cathode gap size of 3 mm wasconstructed. This pitch size is almost at the technical limit to allow some space forsoldering. The gap between the anode wires and the cathode planes was determined tobe 3 mm from a balance between preventing the discharge and maintaining the gain witha low operation voltage. The sense wires were a gold-plated 15 µm-diameter tungsten
wire. These anode wires were fixed on the G10 frame with a thickness of 3 mm. In orderto suppress damage of the cathode by discharge, the cathode planes were made of 20µm-thick graphite pasted on 12 µm-thick aramid film.
The assembled structure of the BC1, 2 is shown in Figure 2.10(a). The MWPCs had
6 layers (x, u, v, x, u, v) configuration, where x plane measured the horizontal position.
The u and v planes were tilted by ±15◦ with respect to the x plane. The front-end
read-out electronics for both MWPC and MWDC were made of ASD (Amplifier-ShaperDiscriminator) chips with 16 ns integration time developed for ATLAS Thin Gap Chamber [77]. The timing information of the BC1, 2 hit was digitized by the MWPC encoder
installed in COPPER modules [78].
The gas mixture for both MWPCs and MWDCs was Ar (76%) + C4 H10 (20%) +Methylal (4%). The operation voltages of MWPCs were set to be −2.5 kV.
BC3, 4 (MWDC)
At the exit of the K1.8 beam spectrometer, the wire chambers have to be operated atseveral MHz. Thus, a 3-mm anode-wire-spacing (1.5 mm drift distance) drift chamber
was chosen as BC3. Figures 2.10(b) and 2.10(c) show the structure of BC3. For BC4, weused a drift chamber with the anode wire pitch of 5 mm used in the previous KEK-PS
experiments [79]. For both BC3 and BC4, the sense wire was a gold-plated 12.5 µmdiameter tungsten wire and the field wire was a gold-plated 75 µm-diameter copper-

34

CHAPTER 2. EXPERIMENT

(a)

(b)

(c)

Figure 2.10: (a) Structure of the BC1, 2 (MWPC). (b) Side view of the BC3 (MWDC).
(c) Front view of the wire frame of the BC3 (MWDC) [75].

beryllium wire. The cathode planes of BC3 were made of 20 µm-thick graphite pasted
on 12 µm-thick aramid film. The optimal cathode pitch size was 1.7 mm based on thestudies from the previously used drift chamber with the anode wire pitch of 5 mm. By
considering the manufacturing accuracy, the pitch size was determined to be 2 mm. The
drift chambers have 6 layers (xx′ , uu′ , vv ′ ) as same as the MWPCs. The wire positionof each pair plane was shifted by a half of the cell size to resolve L/R ambiguity. The
timing information of the BC3, 4 hit was digitized by the TKO Multi-hit TDC module.
The BC3 was operated at the cathode and potential wire high voltage of −1.22 kV and−1.25 kV, respectively. In case of BC4, the high voltage of −1.40 kV were applied atboth cathode and potential wires.

2.5. SUPERCONDUCTING KAON SPECTROMETER (SKS)

2.5

35

Superconducting kaon spectrometer (SKS)

Overview
The emitted kaon in the (π + , K + ) reaction was measured by using the superconducting
kaon spectrometer (SKS). The SKS was constructed for the study of Λ-hypernuclei withthe (π + , K + ) reaction [80].
In the present measurement, the SKS magnetic field was set at 2.36T. Design parameters of the SKS at the 2.36 T mode are summarized in Table 2.4. In this mode, emitted
particles in the momentum range of 0.8–1.3 GeV/c with a scattering angle between 2◦
and 16◦ were analyzed. The very forward events (less than 2◦ ) were cut out in order tokeep good vertex resolution and suppress beam-oriented backgrounds in the (π + , K + )events, such as µ+ from π + decay and secondary particles produced from various support structures. By using SKS, the particle momenta were measured with a resolution of
about 0.2% (FWHM) in an acceptance of about 100 msr. In addition, it kept the flightpath as short as 5.5 m for the central trajectory in order to minimize kaon decay-in-flight.
The SKS enables us to realize the high energy resolution and high statistic experiments.
Table 2.4: Design specifications of the SKS spectrometer at the 2.36 T mode.
Maximum magnetic field
Stored energy
Pole gap
Conductor
Ampere Turn
Maximum current
Total weight
Momentum resolution
Momentum range
Bending angle
Solid angle
Flight path

2.5 T
6.3 MJ
49.75 cm
NbTi/Cu
2.1 MA·T
400 A
280 t
0.2% FWHM at 1.1 GeV/c
0.8–1.3 GeV/c◦
85 for central trajectory∼100 msr∼5.5 m for central trajectory

The SKS spectrometer consisted of four sets of drift chambers (SDC1, SDC2, SDC3
and SDC4), a superconducting magnet (SKS magnet), a timing plastic scintillator hodoscope (TOF), a beam veto hodoscope (BVH) and two threshold-type Čerenkov counters (LAC and LC). The kaon momentum was calculated by using the Runge-Kutta
method with a calculated field map. The kaon was identified by time-of-flight between
BH2 and TOF in combination of with the flight-path length for each track. The background particles which were produced after the beam hit the SDC4 support frame were
suppressed by using the BVH plastic scintillator hodoscope at the trigger level. In order to reduce multiple scattering eﬀects on the momentum resolution, helium bags were
installed in the spaces along the particle trajectory (the SKS pole gap and the space
between SDC3 and the SKS magnet). The magnetic field was monitored with an NMR

36

CHAPTER 2. EXPERIMENTSSD DC2
C1
BH RC
A
BC 2
BC 4
3

SKS Magnet

TOF

LC

SDC4
BVH
SDC3

probe during the experiment to correct for the fluctuation of the field in the oﬄine
analysis. The accuracy of the NMR probe is 1.0 × 10−6 [81].

Target
LA
C

0

Q13
Q12

3m

Figure 2.11: Schematic view of SKS. SDC1–4 were drift chambers. TOF was a plastic
scintillation counter hodoscope for the time-of-flight measurement. LAC was aerogelČerenkov counter (n=1.05). LC was a Lucite (Acrylic) Čerenkov counter (n=1.49).
RCA was installed surrounding the target in order to detect the decayed particles.

2.5. SUPERCONDUCTING KAON SPECTROMETER (SKS)

37

Trigger counters
Specifications of the trigger counters in SKS are listed in Table 2.5. In the trigger, acombination of three kinds of trigger counters were used to identify pions, kaons andprotons. The TOF counter is sensitive to all charged particles, LAC are sensitive only
to pions, and LC is insensitive to protons.
Table 2.5: Specifications of the particle identification counters in the SKS spectrometer
Name Sensitive area
Specification
PMT
W×H×T (mm)(Hamamatsu)
TOF 2240×1000×30 32 segments
H1949
LAC 1050×1200×113 Aerogel; n=1.05
R1584-02, (Burle)-8854
LC
2800×1400×40 28 segments, Acrylic; n=1.49 H1949, H6410
BVH 240×150×5
4 segments
H6524MODTOF
TOF is a segmented plastic scintillation hodoscope located at just a downstream of SDC4
to identify scattered particles by the time-of-flight measurement with BH2. Figure 2.12
shows a schematic view of TOF. The TOF counter was horizontally segmented into 32
pieces of 70×1000×30 mm3 scintillators. The signal of each segment was detected byphototubes (H1949) on the top and bottom sides. A typical time-of-flight resolution
between TOF and BH2 was measured to be 150 ps (rms). This is suﬃcient to separate
the scattered pions, kaons and protons.

38

CHAPTER 2. EXPERIMENT

c
XTOF

ZTOF

30 mm

YTOF 70 mm

c1000 mmc

Front viewc

Top view

O

Beam
Segment
Number 32 31 30 29

c

18 17 16 15

c

3 2 1

Scintillator
BC410
Acrylic Light Guide
Hamamatsu H1949

Figure 2.12: Schematic view of TOF.

LAC
LAC is a threshold-type silica aerogel Čerenkov counter to select kaons in the trigger
level. As shown in Figure 2.13, pions with a threshold of 0.45 GeV/c were rejectedby the reflactive index of silica aerogel of 1.05. LAC was installed just behind of the
TOF counter. Figure 2.14 shows a schematic view of LAC. The sensitive area of LAC
was 1050×1200×113 mm3 . For the uniform eﬃciency without any dead space overa large sensitive area, LAC was not segmented but of a large one-box type. 5-inch
phototubes (Hamamatsu-R1584 and Burle-8854) which were sensitive to a single photon
were placed on both sides. The number of photo electrons was typically 6 over the wholearea for scattered pions at 0.9 GeV/c.

Reflactive index

2.5. SUPERCONDUCTING KAON SPECTROMETER (SKS)39

1.6
Lucite

1.5

p

1.4

Water

1.3
K

1.2
π

1.1
1
0.9
0.2

Aerogel

e
0.4

0.6

0.8

1

1.2
1.4
Momentum [GeV/c ]Figure 2.13: Threshold and refractive index for Čerenkov radiation as a function of the
momentum.

Figure 2.14: Schematic view of LAC.

40

CHAPTER 2. EXPERIMENTLC
LC is a threshold-type Čerenkov counter installed just downstream of LAC. Figure 2.15
shows a schematic view of LC. It was segmented into 28 vertical pieces of 100×1400×40
mm3 Lucite (Acrylic) radiator with the reflection index of 1.49. Each segment is equippedwith fast phototubes (H1949) on the top and bottom sides. As shown in Figure 2.13,
most of protons slower than 0.85 GeV/c were rejected.

cTop view

ZLC

40 mm
100 mmXLC

c

1400 mmc

Front view

YLC

O
Beam

Segment
Number 28 27 26 25

c

16 15 14 13

c

3

2

1

Lucite +bisMSB

Acrylic Light
Guide
Hamamatsu
H1949
Figure 2.15: Schematic view of LC.

2.5. SUPERCONDUCTING KAON SPECTROMETER (SKS)41

BVH
BVH is a segmented plastic scintillation hodoscope located at just upstream of SDC4
to reduce the background trigger rate. Figure 2.16 shows a schematic view of BVH.
BVH was horizontally segmented into 4 pieces of 60 × 150 × 5 mm3 scintillators. Phototube (H6524MOD), which was same as BH1 and 2, was connected on bottom side ofeach segment.
Figure 2.17 shows the typical trajectories of the background particles produced after
the beam hits the SDC4 frame and made fake triggers. The green arrows show the typicaltrajectories of these background particles. BVH was installed on the beam trajectories
at pπ+ = 1.69 GeV/c as shown in Figure 2.17.

Beam
Scintillator
BC410
Acrylic Light Guide
Hamamatsu
H6524MOD

5

X

150

240

60

Figure 2.16: Schematic view of BVH.

42

CHAPTER 2. EXPERIMENTSKS
Magnet
BVH
Targetπ+ beam at 1.69 GeV/c(path through the target)

SD

C4
TO
F

K+
LC

Backgroundfrom SDC4 frame

Figure 2.17: Typical trajectories of the background particles. The beam trajectories in
the SKS with beam momentum of 1.69 GeV/c are shown in orange lines. The backgroundparticles were produced after the beam hits the SDC4 frame and made fake triggers, as
shown in green arrows. Typical tracks of emitted K + are also shown in black lines.

Tracking chambers
Specifications of the tracking chambers of the SKS are summarized in Table 2.6.

SDC1, 2At the entrance of the SKS magnet, two sets of drift chambers (SDC1 and SDC2) were
installed. SDC1 was the same as BC3 except that it has four layers (v, v ′ , u, u′ ) configuration. The SDC2 was similar to SDC1 except for its wire spacing, the anode wire pitchof SDC2 was 5 mm. For both SDC1 and SDC2, the sense wire was gold-plated 12.5µm-diameter tungsten wire, and the field wire was gold-plated 75 µm-diameter copperberyllium wire, and the cathode planes were made of 20 µm-thick graphite pasted on 12µm-thick aramid films. The SDC2 had 6 layers of xx′ , uu′ , vv ′ , where u and v wires weretilted ±15◦ with respect to the x wires. Since the SDC1 and SDC2 were in line withthe beam, the gas mixture and read-out electronics were the same as those of beam line
chambers.

2.5. SUPERCONDUCTING KAON SPECTROMETER (SKS)

43

Table 2.6: Specifications of the drift chambers of the SKS.
Name
SDC1
SDC2
SDC3
SDC4

Area
Anode pitch or
W×H (mm) Drift length (mm)192×100
1.5
400×1502.5
2140×1140
10
2140×1140
10

Wires
vv ′ uu′
vv ′ uu′ xx′
vxuvxuvxuvxuAngle (x, u, v)
Resol.
◦()(µm in r.m.s)
0, +15, −15
200
0, +15, −15
200
0, +30, −30
300
0, +30, −30
300

Gas mixture (SDC1, 2); Ar(76%) + C4 H10 (20%) + Methylal(4%)
Gas mixture (SDC3, 4); Ar(50%) + C2 H6 (50%)
SDC3, 4Large-sized drift chambers (SDC3, 4) were installed at the exit of the SKS magnet. These
drift chambers, which had been used in the BNL-AGS experiment [82], were moved to
J-PARC. The size of the eﬀective area was 2140×1140 mm2 , being twice larger in lengththan in the previous SKS one. All anode wires were replaced to the larger diameter(20µm → 25µm) wires for more strength. The drift space was 10 mm and its cellstructure is shown in Figure 2.18. The high voltage of potential wires was set at −350
V and −450 V and the anode high voltage was applied at +2.2 kV. The anode wire wasa gold-plated 25 µm-diameter tungsten wire, and both field wire and cathode wire weregold-plated 80 µm-diameter copper-beryllium wire. The pith of the cathode wires was 2mm. SDC3 and SDC4 had 6 layers (x, x, u, u, v, v), where u and v wires were tilted ±30◦with respect to the x wires. The front-end read-out electronics of SDC3, 4 was made of
ASD chips. The timing information of the SDC3, 4 hit was digitized by the TKO Dr.TII
TDC module

Cathode (GND)
Potential (-450 V)
Potential (-350 V)

12 mm
Anode (~+2200 V)

Drift length

Potential (-450 V)

20 mm

Figure 2.18: The cell structure of SDC3, 4.

44

2.6

CHAPTER 2. EXPERIMENT

Liquid hydrogen and deuterium target

In order to use pure proton and deuteron targets, we used the liquid target system which
was used in the KEK E559 experiment [83]. A liquid deuterium target of 1.99-g/cm2
thickness was used for the d(π + , K + ) reaction at 1.69 GeV/c, and a liquid hydrogentarget of 0.85-g/cm2 thickness for the p(π + , K + ) reactions at 1.58 and 1.69 GeV/c for
calibrations. Specifications of the liquid hydrogen and deuterium target were listed inTable 2.7.
Table 2.7: Specifications of the liquid hydrogen and deuterium target.
Size
Capacity
Material
Average thickness
Target chamber
Vacuum
LH2 thickness
LD2 thickness
Mylar thickness

ϕ67.3×120L mm
427 cm3
PET(cylinder), Mylar(end cap)
0.3 mm(cylinder), 0.25 mm(end cap)
Aluminium; t=3 mm, ϕ270 mm
Window(Mylar); t=0.25 mm∼ 1.0 × 10−7 mbar
0.85 g/cm2 (0.0708 g/cm3 ×12 cm)
1.99 g/cm2 (0.166 g/cm3 ×12 cm)
0.0695 g/cm2 (1.39 g/cm3 ×0.025 cm×2)

Figure 2.19 shows a schematic view of the liquid hydrogen target. The target shape
was cylindrical; 67.3 mm in diameter and 120 mm in length. The target fully covered the incident beam with a typical beam size of σH = 7.6 mm (horizontal) andσV = 4.2 mm (horizontal). Its cooling system uses liquid helium. The hydrogen vessel
was made from PET (polyethylene terephthalate) of 0.30 mm thickness for the cylinderpart, and Mylar of 0.25 mm thickness for the end cap. The pressure of the target wasmonitored during the experimental period.

2.6. LIQUID HYDROGEN AND DEUTERIUM TARGET

45

Target chamber

Target cellMylar
(t=0.25)

Mylar(t=0.25)
Mylar
0.25

PET ( f 67.8, t=0.3)

Mylar
Mylar
(t=0.25)
0.25

t=3
AlAl.
(t=3)

Mylar
(t=0.25)

Figure 2.19: Schematic view of the liquid hydrogen and deuterium target (units in mm).

46

CHAPTER 2. EXPERIMENT

2.7

Range counter array (RCA)

In the d(π + , K + ) reaction, there are background processes of quasi-free hyperons (Λ andΣ’s), hyperon resonances (Λ(1405) and Σ(1385)’s) and non-resonant (Λπ and Σπ) productions. Thus, we have to reduce these background processes by detecting the decay
particles of the K − pp. The K − pp is expected to decay to non-mesonic modes such as Λpand Σ0 p. In such non-mesonic decays of the K − pp, a proton or two protons can be produced as “K − pp”→ Λp → pπ − p. On the other hand, a proton can be produced from thedecay of hyperon such as Λ → pπ − in the quasi-free processes (background). Moreover,a proton can be also produced as a spectator in the quasi-free backgrounds. However,the proton kinematics between the K − pp and quasi-free backgrounds is diﬀerent.
Figure 2.20 (a) shows a scatter plot between momentum and scattering angle in xz
plane, where x and z coordinates correspond to the horizontal and beam directions, ofthe proton from the decay of Λ in one of the quasi-free processes of π + “n”→ K + Λπ 0
reaction. Figure 2.20 (b) shows the same scatter plot of the proton from the “K − pp”→
Λp → pπ − p mode. As shown in these figures, the proton’s scattering angle in thequasi-free background processes concentrates in the forward angle. On the other hand,the proton produced from the K − pp decay such as K − pp → Λ(Σ0 )p can distributein a wide scattering-angle region. Moreover, the proton’s momentum of the spectator
is small (pproton ≲ 250 MeV/c). Almost all the spectator protons would stop in the
deuterium target. Thus, we can reduce the quasi-free background processes by measuring
the large scattering angle and high-momentum proton. Furthermore, we can detect theK − pp signal free from the quasi-free backgrounds by measuring two protons in large
scattering angles.
-(a): π+"n" → K+Λπ0, pπ-π0
180

180
180
160

140
140

Seg3, 6

120

100
80
60

100

Seg2, 580
60

Seg1, 4

120

80
60

20

20

20

0

0
0

400

600

800

1000

Momemtum of proton [MeV/c]

100

Seg3, 6

100

40

200

120

140

40

0
0

140

160

θxz of proton [degree]θxz of proton [degree]

160

120

-

(b): K pp → Λp, pπ p80Seg2, 560

Seg1, 4

40

40

20

200

400

600

800

1000

0

Momemtum of proton [MeV/c]

Figure 2.20: (a) Scatter plot between momentum and scattering angle in xz plane ofthe proton from the typical quasi-free process of π + “n”→ K + Λπ 0 , Λ → pπ − . In (b), thesame scatter plot for the K − pp → Λp, Λ → pπ − reaction is shown. The acceptance foreach segment of RCA is also shown with red boxes. These correlation plots were madefrom a Monte Carlo simulation.

2.7. RANGE COUNTER ARRAY (RCA)47

In the E27 experiment, we installed the six range counter arrays (RCA’s) surrounding
the liquid target system to detect the proton from the K − pp. The six range counter arrays
composed of three in the left (Seg1 to Seg3) and three in the right (Seg4 to Seg6) of thebeam (z) axis as shown in Figure 2.21. According to our simulation, the proton fromthe quasi-free background can not produce in scattering angle θxz(Lab) ≳ 70◦ as shownin Figure 2.20 (a). Thus, the Seg2 and 5 of RCA was installed at θxz(Lab) ≳ 70◦ . Notethat the forward segments (Seg1 and 4) of RCA conflict to the SDC1 and 2, especially
support frame of SDC1 and 2, geometrically. Therefore, in order to install the RCA at
the forward angle, we have to move the target position backward. On the other hand, theK + acceptance of the SKS strongly depends on the target position. The K + acceptancebecomes small when we move the target position backward. Finally, we determined
the target and RCA positions to optimize the acceptance of K + and proton(s). In thisexperiment, the RCA was installed in the laboratory angles (θxz(Lab) ) between 39◦ and122◦ as shown in Figure 2.21. Its geometrical coverage was about 26%.

㻟㻥
㼻

㻙㻝
㻞㻞
㼻

㻿㻰㻯㻞
㻿㻰㻯㻝

K+(SKS)

㻿㼑㼓㻝

㻡

㼙
㻜㼏

㻿㼑㼓㻠

㻿㼑㼓㻡

㻿㼑㼓㻞

㼀㼍㼞㼓㼑㼠
㻿㼑㼓㻢

㻿㼑㼓㻟

0

50 cm

+

π (K1.8)

㻾㻯㻭Figure 2.21: Schematic view of the range counter system (RCA) in the xz plane. It wascomposed of six range counter arrays; three in the left (Seg1 to Seg3) and three in theright (Seg4 to Seg6) of the beam axis.

Each range counter array had five layers of plastic scintillation counters; the thicknessof each scintillator was 1 cm, 2 cm, 2 cm, 5 cm and 2 cm, respectively, with a height of
100 cm. The width of each layer was 20 cm. Schematic view of the one unit of range
counter array is shown in Figure 2.22 (a). The first two layers were segmented into two
slabs; each slab had 10-cm width. Therefore, we had seven (2+2+1+1+1) scintillation
counters in one range counter array. Every scintillation counter was read out from bothsides (up and down) by a phototube; H1949 was used for the first layers and H6410 was

48

CHAPTER 2. EXPERIMENT

(b)

60

50
20

44.5

p

π

range [mm]

60

20

(a)

45

20
10

100

100

β

Figure 2.22: (a) Schematic view of one unit of range counter array. (b) The
range as a function of β for the pion and proton. The thickness of range counter(10+20+20+50+20) mm are also indicated with a dashed-line.

used for the other layers.
From each PMT, both hit timing and pulse height information was obtained. The
discriminator threshold for the timing information was set at less than the one tenthlevel of the minimum ionizing particles. The timing information from the first layer wasused for the on-line trigger and the time-of-flight analysis in oﬀ-line. The distance fromthe liquid target center to the first layer was about 50 cm.
The time-of-flight (TOF) of each particle was obtained with the hit timing in thefirst layer with a resolution of 160 ps. The flight path length was measured from thevertex position of the (π + , K + ) reaction to the hit position on the first layer, which was
obtained with the time diﬀerence between the up and down PMT’s. Then, the velocityof the particle (β) was obtained as β = (path length)/(TOF·c), where c is the light speed.
Moreover, we can define the stopping layer, istop , for each range counter array from a hit
pattern of five layers.
Figure 2.22 (b) shows the range as a function of β for the pion and proton. The
thickness of our range counter (1+2+2+5+2) cm are also indicated with a dashed-line
in this figure. We can separate the pion and proton by using the information of the
stopping layer and the velocity of particles.
Furthermore, in order to improve the separation between pion and proton, we set up
a particle identification parameter, P ID, as,()
f istop + dE
f (i −1) )α − (dEf istop )α · cos θ,
P ID = (dE
(2.1)
stop
f i shows the energy deposit in the i-th layer of the plastic scintillators and θ iswhere dEthe incident angle for RCA. The α is the constant parameter, where ∼1.75 is empiricallyused. The P ID corresponds to the range of the previous layer of the stopping one andit should depend on not momentum but charge and mass of the particle. Finally, theproton was selected by combining the information of the stopping layer, the velocity and
the P ID.

2.8. TRIGGER

2.8

49

TriggerIn the (π + , K + ) reaction, many background particles are produced through the pionnucleon reactions, such as (π + , p)X and (π + , π + )X reaction. Typical cross sections ofsuch background reactions are two or three orders of magnitude larger than that of the(π + , K + ) reaction. Moreover, π + → µ+ + νµ decay in flight was not trivial to make thefake trigger. Therefore, a powerful trigger system is very important.
In the present experiment, we used two main triggers: the (π, K) inclusive trigger andthe (π, K) coincidence trigger. In both triggers, the 1st level trigger, TOF-LC matrix
trigger and 2nd level mass-trigger systems were introduced. These triggers are describedlater in this subsection. The inclusive trigger was prescaled 1/3 in order to decreased a
trigger rate. The trigger logic diagram of these main triggers are shown in Figure 2.23.
Prescaled beam trigger, (π, π) trigger, unbiased (π, K) trigger and TOF-RCA trigger as
the calibration trigger were mixed into them.
RCA

BVH

Coincidence
Trigger(π, K)
Trigger

1st level
Coincidnce Trigger
1st level
Inclusive Trigger

pre scale
1/3

Mass Trigger
System

2nd level
Trigger

1st level clear

LAC
LAC
LAC

-

Figure 2.23: Trigger logic diagram of the (π, K) inclusive trigger and the (π, K) coincidence trigger.

The 1st level trigger
The 1st level trigger of (π, K) inclusive trigger was comprised of a π beam part, anoutgoing K part and the TOF-LC matrix trigger.
The π beam part was defined as:
BEAM ≡ GC × BH1 × BH2.

(2.2)

BH1 an BH2 had two PMTs at both end, and then mean timer modules were used toremove the incident position dependence of the trigger timing. The coincidence timing

50

CHAPTER 2. EXPERIMENT

between BH1 and BH2 was adjusted with a coincidence width less than 5 ns. The
proton contamination was completely rejected by precisely adjusting the coincidence
timing between BH1 and BH2 for pions. This was possible for the momentum of lessthan 1.5 GeV/c, which corresponds to the time diﬀerence between BH1 and BH2 of ∼7
ns.
The outgoing K part was defined as:
KOU T ≡ T OF × LC × LAC × BV H.

(2.3)

Mean timer modules were also used for the same reason for the TOF and LC counters.
Finally, the 1st level (π, K) inclusive trigger was defined as:
P IK ≡ BEAM × KOU T × M AT RIX,

(2.4)

where M AT RIX was the TOF-LC matrix trigger.
The 1st level (π, K) coincidence trigger was additionally required at least one hit
among 12 first-layer scintillators of RCA, which also used mean timer modules for thesame reason, as:P IK(COIN ) ≡ P IK × RCA.
(2.5)
By requiring the hit of RCA, the trigger rate could be decreased about 1/4 and it helped
to reduce the DAQ dead time.
The BH2 timing was used as the STOP signal of the TDC’s for BCs and SDC1, 2,
while the TOF timing was used as the stop signal for SDC3, 4 because the flight timefrom BH2 to TOF varies according to the flight path and momenta of scatted particles.

TOF-LC matrix trigger

LC Segment

25
20
15
10
5
5

10

15

20

25

30

TOF Segment

Figure 2.24: The hit patteren of TOF and LC segments without the matrix trigger. The
selected TOF and LC segment region for the matrix trigger was indicated in red lines.

2.8. TRIGGER

51

The matrix trigger was generated when the appropriate hit combinations between
TOF and LC segments were matched. For constructing the matrix trigger, we used an
FPGA module called TUL (Tohoku Universal Logic Module) [85]. Figure 2.24 shows hit
patteren of TOF and LC segments without the matrix trigger. In the figure, the selected
region is also indicated with solid lines and the background events are located out of theregion. The 1st level (π, K) trigger was reduced by 30% with the matrix trigger.

The 2nd level mass trigger
The outgoing proton was roughly rejected by using the 2nd level mass trigger system.
The momentum of the outgoing particles were correlated to the horizontal direction
cosine (dx/dz) at SDC3, 4 position. The dx/dz was roughly estimated with the hit
combination of TOF and LC segments as shown in Figure 2.25. Then, the mass of theoutgoing particle was estimated with their time-of-flight between BH2 and TOF andmomentum by the hit combination of TOF and LC segments.

1200

Tof# = 8
Tof# = 8, Lc#= 1
Tof# = 8, Lc#= 2
Tof# = 8, Lc#= 3
Tof# = 8, Lc#= 4
Tof# = 8, Lc#= 5Tof# = 8, Lc#= 6
Tof# = 8, Lc#= 7Counts

1000
800
600
400
200
0
-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

dx/dz SDC34 track

Figure 2.25: The horizontal direction cosine at SDC3, 4 position for each hit combinationof TOF and LC segment in each color. The color lines for each corresponding segment
are listed in the figure. The horizontal direction cosine could be determined by checking
with the hit combination of TOF and LC segment roughly.
The emitted K + was selected by setting a suitable window against time-of-flightbetween BH2 and TOF for each hit combination. Typical accepted and rejected region
are shown with red and black lines, respectively, in Figure 2.26. Almost half of outgoingprotons could be rejected by using the mass-trigger system.
The trigger scheme for the mass trigger is illustrated in Figure 2.27. This mass trigger
system was introduced to the P IK and P IK(COIN ) triggers. The timing informationof the TOF signals was digitized with a LeCroy 4303 TFC (Time-to-Fera Converter)
module.
The hit addresses and the timing information of TOF were stored in the memories in
the FERA driver, and the hit information of LC was stored in TUL. The FERA driver

52

CHAPTER 2. EXPERIMENT

0dx/dz SDC34 track

-0.1
-0.2

(a)

-0.3

1000

800

K

π

-0.4
-0.5

p

600

400

-0.6
-0.7

200

-0.8
-0.9
18

20

22

24

26

28

30

0

Time-of-fligt BH2-TOF [ns]

4500
4000
3500

(b)

p

π

Selected event

Counts

3000

Clear event

2500

K

2000
1500
1000
500
0
18

20

22

24

26

28

30

Time-of-fligt BH2-TOF [ns]Figure 2.26: (a) The scatter plot between the (dx/dz) obtained from SDC3, 4 tracking
and the time-of-flight between BH2 and TOF when we required the hit of TOF 4 segment
and LC 2 segment. The outgoing pions, kaons and protons are seen in this figure. (b)The accepted and rejected region are shown with red and black lines, respectively. In
this figure, we also required the hit of TOF 4 segment and LC 2 segment.
sent the 4 bits of hit address information and 9 bits of time-of-flight information to TUL.
If the time-of-flight of TOF was in the time window we set the 2nd level (π, K) trigger.
If not, the 1st-level trigger clear signal was generated and all the stored data in each
DAQ modules were cleared. The decision time of the mass trigger was about 15 µs.

2.8. TRIGGER

53
1st level (π,K) trigger

LC

TOF

1ch ... 28ch

1ch ... 32ch

TUL

TFC

hit combination+ TDC cut

TDC data

FERA driver

Hit Address(4 bit)
+ TDC data(9 bit)
2nd level (π,K) trigger

Figure 2.27: Logic Scheme of the 2nd-level mass trigger.

Calibration triggers
In order to monitor the eﬃciency of each detector and adjust the calibration parameters,
calibration triggers were mixed with prescale factors in the main trigger. These calibration triggers mean the beam, (π, π), unbiased (π, K) and TOF-RCA triggers definedas:
P IP I ≡ BEAM × T OF × LC,
P IK(unbiased) ≡ BEAM × T OF × LC × LAC,T OF −RCA ≡ BEAM × T OF × RCA.

(2.6)
(2.7)
(2.8)

The prescale factors were 1/(256 × 256 × 2) for the beam trigger, 1/(256 × 30) for the(π, π) trigger, 1/100 for the unbiased (π, K) trigger and 1/500 for the TOF-RCA trigger.
The 2nd-level mass trigger system was not used for these calibration triggers.

54

2.9

CHAPTER 2. EXPERIMENT

Data-acquisition system

-

-

-

Figure 2.28: The diagram of the data-acquisition system.
Figure 2.28 shows a diagram of the data-acquisition system. The raw signals of RCA,
trigger counters and SDC3, 4 were digitized with the TKO TDC and ADC modules andthe TKO TDC (Dr.TII) modules, respectively, while the signals of BC3, 4 were digitizedwith the TKO Multi-hit TDC (MHTDC) modules. For the TKO modules, those digitizedsignals were transfered to the VME-SMP (Super Memory Partner) which was installed inthe VME box together with a VME-CPU module. The data were read out by the VMECPU module and transfered to the host computer. The timing information of the BC1,
2 hit was digitized by the MWPC encoder installed in the COPPER modules. COPPER

2.9. DATA-ACQUISITION SYSTEM

55(COmmon Pipelined Platform for Electronics Readout) [78] is a new platform module forthe KEK-VME specification that realizes various types of analog-to-digital conversion
and pipelines digital data processing functions within a unified scheme. Although the
COPPER is a VME slave module, it works as a standalone system without any additional
VME processor on the VME bus. The BC1, 2 data on the COPPER modules weredirectly transfered to the host computer. The data-acquisition cycle was processed eventby event. The single counting of each trigger counter was recorded by VME scalers,
which were transfered at the end of spill.
For the early stage of J-PARC hadron experiments, we needed to use several conventional DAQ subsystems, such as TKO, together with a new network oriented DAQ
module, KEK-VME/COPPER. It was necessary to integrate these diﬀerent data acquisition readouts. In addition, most readout systems (VME-CPU and COPPER) have
network interfaces and communicate via the TCP/IP protocol. Under this situation, wedeveloped a network-based DAQ system [86] with a DAQ software using the TCP/IP
protocol and a trigger/tag distribution system.
For building up an event by combining data sets coming from the diﬀerent modules,
we needed to write the event number and the spill number to each data set and to checktheir consistency event by event in the event building. For this purpose, we developeda trigger/tag distribution system. When the trigger signal was generated, the Master
Trigger Module (MTM) accepted the trigger signal and distributed the event and spill
numbers to Receiver Modules (RM) in each node by using the Ethernet cables. After
finishing the analogue to digital conversion of all the modules in each node, MTM distributed the read-out signal to all the RMs and the event data with the same event andspill numbers were transfered to the host computer. The event and spill numbers were
distributed to the data bus by RM in each node. The information of those numbers weretransfered together with the digitized raw data to the host computer. However, in thepresent experiment, we did not use these event and spill numbers for an event buildingin the host computer, because the data read-out was successfully carried out without
any event slipping.
The data transfered from each module to the host computer were at first processedby the Event-Builder. Then they were transfered to the Event-Distributor and to downstream processes.

56

CHAPTER 2. EXPERIMENT

2.10

Data summary

The K − pp production data of the d(π + , K + ) reaction at 1.69 GeV/c was taken in June2012 as listed in Table. 2.8. The total number of pions irradiated on the liquid deuterium
target was 3.3×1011 .
In this experiment, we took beam-through data at beam momentum of 0.9 GeV/cwith and without experimental target and p(π + , K + )Σ+ data with liquid hydrogen target
at pπ+ = 1.58 GeV/c for calibrations. This beam momentum was selected in orderto have a good overlap of the kinematics of K + in the Σ+ production reaction withthe d(π + , K + )K − pp reaction. Furthermore, we measured the p(π + , K + ) reaction at
1.69 GeV/c, which is the same beam momentum of K − pp production, by using theliquid hydrogen target. We adjusted the missing-mass scale of the d(π + , K + ) reactionand evaluated the missing-mass resolution by using these data. In addition, we could
check the validity of energy calibration and cross section normalization by looking at theΣ+ mass and cross sections because these values were well known.
Table 2.8: Summary of the obtained data with diﬀerent combinations of experimental
targets, incident π + momenta Pbeam , and beam intensities. Nbeam means the total numberof π + beam irradiated on the target.
Reactiond(π + , K + )p(π + , K + )p(π + , K + )Σ+beam-throughTarget Thickness
Pbeam[g/cm2 ][GeV/c]
LD2
1.99
1.69
LH2
0.85
1.69
LH2
0.85
1.58
none
−
0.9

Beam intensity
Nbeam[pion/spill]3.0-3.3×106
3.3×1011
3.0×106
7.6×1096
3.0×101.2×109
∼ 104
∼ 105

Chapter 3
Analysis I - inclusive analysis
The data analysis can be separated into two parts, namely the analysis of the magnetic
spectrometers and the coincidence analysis of the RCA. The analysis of the K1.8 beamline spectrometer and the SKS is described in this chapter. The goal of this part is toobtain a missing mass spectrum of the (π + , K + ) reaction as an inclusive spectrum. The
analysis of the RCA for the coincidence measurement is described in the next chapter.

3.1

OutlineA missing-mass spectrum is obtained as a double diﬀerential cross section ofd2 σ̄θ1 –θ2 /dΩ/dM averaged over the scattering angle of the (π + , K + ) reaction from θ1
to θ2 . The double diﬀerential cross section is calculated as:ANπK
d2 σ̄θ1 –θ2=,dΩdM
NA (ρx) Nbeam ∆Ωθ1 –θ2 ∆M ϵ

(3.1)

where A is the target mass number, NA the Avogadro constant, ρx the target mass
thickness, NπK the number of good (π + , K + ) events in the missing-mass interval ∆M ,Nbeam the number of beam pions on the target, ∆Ωθ1 –θ2 the solid angle of SKS between
θ1 and θ2 and ϵ the overall experimental eﬃciency. In the whole oﬄine analysis, the errorof eﬃciency is estimated for the systematic uncertainty. The statistical error is negligibly
small compared with the systematical one. The mass of the produced particle (M Md )in the d(π + , K + )X reaction is obtained as a missing mass by calculating the following
equation in the laboratory frame√(3.2)
M = M Md = (Eπ + Md − EK )2 − (p2π + p2K − 2pπ pK cos θπK ),where Eπ and pπ are the total energy and momentum of a pion, EK and pK are those of akaon, Md is the deuteron rest mass, and θπK is the scattering angle of the reaction. Thus,
we need to measure three kinematic variables, pπ , pK and θπK , through the momentum
reconstruction.
Figure 3.1 shows a flowchart of the oﬄine analysis. First, good (π + , K + ) events should
be distinguished from a large number of background events. We request all counters havegood hits and an incident beam π + is selected by using the time-of-flight between BH157

58

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

and BH2 within the time window of ±2 ns. The emitted K + is roughly selected by using
the information of the TOF, LC counters combining with the tracking information in
SDCs. Then, the beam π + momentum and emitted kaon momentum are reconstructedwith the K1.8 beam line spectrometer and SKS, respectively. For each spectrometersystem, a local track assuming the straight line is selected using the hit positions of the
tracking chambers installed both at the entrance and exit of the spectrometer. Then
good tracks are selected by connecting those local track candidates so as to give theleast chi-squares in the track reconstruction. For the track reconstruction of the K1.8
beam spectrometer, a third-order transfer matrix is used. In the track reconstruction of
SKS, we used a calculated magnetic field map for the Runge-Kutta tracking method [88].
After the track reconstruction, the final identification of K + is carried out by using thetime-of-flight with the flight path and the reconstructed momentum of SKS. Then, avertex point of the (π + , K + ) reaction event is reconstructed from the trajectories of theπ + and K + . Thus, the missing mass is obtained.
Finally, we obtained the missing-mass spectrum as a double diﬀerential cross sectionof d2 σ̄/dΩ/dM after correcting the eﬃciency of detectors and the acceptance of the SKS
spectrometer. These analysis results are described in this chapter.

3.1. OUTLINE

59

New Event

Hodoscope Analysis
・All counters have good hits
・|Beam TOF| < 2ns

BH1 Filter
BC1&2
Local Tracking

BC3&4
Local Tracking
χ2<20

2

χ <20

SDC3&4
Local Tracking

SDC1&2
Local Tracking
χ2<20

χ2<20

Matching of
BH2 time0 Segment
K1.8
Global Tracking

NTrack = 1

TOF & LC Cut

χ2<20

SKS
Global Tracking
χ2<30Good beam
π event

PID: K selected
NTrack of K = 1

Good
K event

Vertexreconstruct
θπK(Lab) > 2°

Good vertex point in the target region

Calculate the missing mass
Correct the acceptance of the SKS
and efficiencies of detectors
Calculate the double differential cross section

Figure 3.1: Flow chart of the oﬄine analysis for inclusive (π + , K + ) spectrum.

60

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

3.2

Analysis of π + beam

3.2.1

Identification of triggered beam particles

Nbeam in Eq. 3.1 is the number of triggers of BH1 × BH2 × GC. The incident hadron
beam such as pion, kaon and proton was separated with the electro static separator(ESS1, 2) written in Sec. 2.2. In addition, the positron was rejected by requiring no hitof the GC at the trigger level. Figure 3.2 show the time-of-flight spectrum between BH1and BH2 with the flight pass of 10.4 m. The flight time diﬀerence between pion and kaonis 1.3 ns for the momentum of 1.69 GeV/c and that of pion and proton is 4.9 ns. Thus,
we found that the proton and kaon in π was rejected in the electro magnetic separator
and time-of-flight. We set the time window, ±2 ns, as shown in Figure 3.2 in order tokeep a π detection eﬃciency. The beam TOF eﬃciency which is the analysis eﬃciencyof time-of-flight cut between BH1 and BH2 (|Beam TOF| < 2 ns) was estimated to be
99.6 ± 0.1 (syst.) %1 . The systematic error was estimated from the fluctuation of theeﬃciency during the experimental period.
The main background of the π + beam was µ’s from the π → µ decay in flight inside
the QQDQQ magnet. The contamination of the background was estimated by checking
the y profile at BC4 as described in Sec. 3.2.4.

14000
12000

Counts

10000
8000
6000
4000
2000
0
-5

-4

-3

-2

-1

0

1

2

3

4

5

Beam TOF [ns]Figure 3.2: Typical time-of-flight spectrum of the incident beam particles. The selected
time window was indicated by arrows.

1

We found that this factor became worse (∼90%) in a few experimental periods. This eﬀect wascorrected to calculate the double diﬀerential cross section.

3.2. ANALYSIS OF π + BEAM

3.2.2

61

BC1 and BC2 local tracking

The BC1 and BC2 were MWPCs installed at the entrance of the K1.8 beam line spectrometer. In the BC1, 2 local tracking, hits on adjoining wires within a proper timing
was made up as a cluster hit. Timing information of BC1, 2 was digitized by the MWPC
encoder with the sampling time interval of 10 ns (100 MHz sampling). In the digitalization, both leading edge and trailing edge information of raw signals were recorded formaking up cluster hits. In the present analysis, the time gate for the leading edge timingwith a 80 ns was set for the clustering. For the tracking analysis, the central position
in a cluster was used. In finding the BC1, 2 track, we applied the hit position gate foreach layer by checking consistency of hit position with the BH1 hit segment. We call thistracking method as BH1 filter tracking. The detail of BH1 filter tracking is described inAppendix A.
Local straight track fitting was performed by using the least squares method. The
tracking χ2 was defined as:
2

χ

)2
12 (
1 ∑ cor − f (zi )=,n − 4 i=1
σi

(3.3)

f (zi ) = x(zi ) cos(θ) + y(zi ) sin(θ),
x(zi ) = x0 + u0 × zi ,y(zi ) = y0 + v0 × zi ,where cor is the position of the cluster center wire σi the position resolution of eachlayer, θ wire tilt angle of each plane (x, u, v for 0◦ , 15◦ , −15◦ ). The optimum parameters(x0 , y0 , u0 (dx/dz), v0 (dy/dz)) which minimize the reduced χ2 were obtained by the leastsquares method.
Figure 3.3 shows a typical reduced χ2 distribution of the BC1, 2 local tracking. In
the local track search, the accepted reduced χ2 value was selected to be less than 20.
Figure 3.4 shows a typical residual distribution of one of the BC1, 2 layers. In
the calculation of the residual in Figure 3.4(a), the calculated layer was included in
the tracking analysis. In case of Figure 3.4(b), the calculated layer was not included.
The intrinsic resolution, σi in Eq. 3.3, was estimated from the geometric average of theresolutions obtained from these two types of tracking. The obtained position resolutionsof BC1, 2 chambers are listed in Table. 3.1.
Table 3.1: The position resolution of each layer.
BC1-Layer resolution [µm] BC2-Layer resolution [µm]BC1-x268.3 ± 1.4
BC2-v
268.7 ± 1.4
BC1-v
267.4 ± 1.4
BC2-u
270.2 ± 1.4
271.6 ± 1.4
BC2-x275.7 ± 1.8
BC1-u
BC1-x
276.9 ± 1.7
BC2-v
272.7 ± 1.4
273.4 ± 1.5
BC2-u271.0 ± 1.4
BC1-v
BC1-u
269.4 ± 1.4
BC2-x
269.1 ± 1.5

62

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

2500

Counts

2000
1500
1000
500
0
0

5

10

15

20

25

30

χ2 of BC1&2 tracking

Figure 3.3: Typical reduced χ2 distribution of the BC1, 2 local tracking. The tracks
were accepted to be less than 20 of the χ2 value.

1400
1200

(a)

700

(b)

600
1000

CountsCounts

500
800
600

400
300

400

200

200

100

0
-2 -1.5 -1 -0.5 0

0.5

1 1.5 2

BC1 residual [mm]0-2 -1.5 -1 -0.5 0

0.5

1 1.5 2

BC1 residual [mm]Figure 3.4: Typical residual distributions of the BC1 layers. (a) The calculated layer
was included in the tracking analysis. (b) The calculated layer was not included in the
tracking analysis. These residual spectra were fitted with a Gaussian function to estimate
the resolution shown in black solid lines.

3.2. ANALYSIS OF π + BEAM

3.2.3

63

BC3 and BC4 local tracking

The BC3 and BC4 were drift chambers installed at the exit of the K1.8 beam line
spectrometer. The drift time information of BC3, 4 was digitized by the TKO Multi-hit
TDC (MHTDC) modules. Figure 3.5(a) and (b) show typical TDC distributions of oneof the BC3 layers (3-mm wire spacing) and one of the BC4 layers (5-mm wire spacing),
respectively.

5000
4500

2500

(a)

4000

(b)

2000

3000

CountsCounts

3500

2500
2000

1500

1000

1500
1000

500

500
800

850

900

950 1000 1050

BC3 Tdc Channel

800

850

900

950 1000 1050

BC4 Tdc Channel

Figure 3.5: Typical TDC distributions of one of the BC3 layers (a) and one of the BC4
layers (b). The TDC distribution was the sum of all hits in a layer, and all multi-hit
signal were shown in the spectrum.
The TDC information was converted to the drift time distribution in order to calculate
the drift length. The origin of the drift timing was roughly determined to the edge of the
TDC distribution (∼1020 ch in Fig. 3.5) and TDC channels (t) were converted to thetime using the MHTDC conversion width of 0.78 ns/ch. The conversion function fromthe drift time to drift length was determined by assuming the uniform hit distribution
with the following equation:∫t
dtDT (t)t0
DL(t) = ∫ tmax
× max drif t length,(3.4)
dtDT (t)t0
DT (t) = (t − t0 ) × 0.78,(3.5)

where t0 is the time origin, tmax is the maximum drift time for the maximum drift
length, and DT (t) is the observed drift time distribution. The maximum drift length
was determined by the wire spacing (3 mm/5 mm).
Figure 3.6 shows a typical scatter plot between the drift time and the drift
length (DL(t)). The scatter plot was fitted by using a 5th-order polynomial function,
which was optimized by minimizing the residual in each plane iteratively.

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

Drift length [mm]

64

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-5

0

5

10 15 20 25 30 35

Drift time [ns]Figure 3.6: A scatter plot between the drift time and the drift length of one of the BC3
layers with the fitting result in black line. The scatter plot was the sum of all hits in alayer.

Before the straight line fitting of BC3, 4, we searched the track candidates in eachlayer. At first, we resolved the left or right (L/R) by checking the hit pattern in thepair plains (x-x′ , u-u′ , v-v ′ ). If the pair plain did not have the corresponding hits, both(L/R) hit positions were considered as the track candidates. All combination of the hit
positions were examined to find a BC3, 4 local track.
Figure 3.8 shows a typical residual distribution of one of the BC3, 4 layers. The
accepted reduced χ2 value was less than 20. Figure 3.4 shows the residual distributionof the tracking. From this distribution, the intrinsic resolutions were estimated as listed
in Table. 3.2. Finally, hit consistency between the track and the BH2 hit segment was
examined.
Table 3.2: The position resolution of each layer.
BC3-Layer resolution [µm] BC4-Layer resolution [µm]BC3-x146.0 ± 0.6
BC4-v
168.6 ± 0.8
150.1 ± 0.7
BC4-v ′
169.4 ± 0.8
BC3-x′
BC3-v
175.1 ± 0.7
BC4-u
186.1 ± 0.8′′
174.0 ± 0.7
BC4-u
194.2 ± 0.9
BC3-v
168.7 ± 0.7
BC4-x
175.6 ± 0.8
BC3-u
′
′
BC3-u
178.3 ± 0.7
BC4-x
196.7 ± 0.9

3.2. ANALYSIS OF π + BEAM

65

2000
1800
1600

Counts

1400
1200
1000
800
600
400
200
0
0

5

10

15

20

25

30

χ2 of BC3&4 tracking

Figure 3.7: Typical reduced χ2 distribution of the BC3, 4 local tracking. The tracks
were accepted to be less than 20 of the χ2 value.

1800
1600

Counts

1400
1200
1000
800
600
400
200
0
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

BC3 residual [mm]Figure 3.8: Typical residual distributions of the BC3 layers fitted with a Gaussian function to estimate the resolution.

66

3.2.4

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

Beam momentum reconstruction

After selecting the straight track candidates at the entrance and exit of the K1.8 beamline spectrometer, those tracks were reconstructed by using the 3rd-order transfer matrix
M calculated by the ORBIT code [87] as follow:⃗ out = M (X
⃗ in , δ),X
dxin dyinX⃗in = (xin , yin ,
,
),
dz dz
dxout dyout,),
X⃗out = (xout , yout ,
dz
dz

(3.6)

⃗ in and X⃗ out are the horizontal and vertical positions and their derivatives at thewhere X
entrance and the exit of the K1.8 beam line spectrometer and δ is momentum deviationfrom the central momentum denoted as p = p0 (1+δ), where p0 is the central momentum.
The momentum of a K1.8 track was determined by minimizing the reduced χ2 value as:

(
)2
(
)2 
12
24
∑
∑
⃗ in )⃗ out )Pi − fi (X1 Pi − gi (X , (3.7)
Hiχ2K1.8 ≡+Hin − 5 i=1
σi
σ
i
i=13
n =

24
∑

Hi ,

i=1


 1 if i−th plane has a hit 

Hi =



0 if i−th plane has no hit,where Pi and σi denote the hit position and resolution of the i-th layer. The calculated⃗ in ) and gi (X⃗ out ).
position by the transport matrix at the i-th plane is denoted by fi (XIn the ORBIT code, the properties of the K1.8 beam line spectrometer magnets suchas the eﬀective magnetic length, aperture, field strength of the central ray, and bending
angle and the radius of central orbit for the dipole magnet were the input parameters.
The eﬀective magnetic length was obtained from a measured magnetic field distribution.
The aperture was taken from the design value of the spectrometer magnets.
After the beam momentum reconstruction, we obtained the beam momentum spectraof 1.69 and 1.58 GeV/c as shown in Figure .3.9. A typical reduced χ2 distribution of theK1.8 tracking at 1.69 GeV/c is shown in Figure 3.10.

3.2. ANALYSIS OF π + BEAM

67

450
14000
12000

(a)

400
350

10000

300

CountsCounts

(b)

8000
6000

250
200
150

4000
100
2000

50

0
1.6 1.621.641.661.68 1.7 1.721.74

01.48 1.5 1.521.541.561.58 1.6 1.62

Beam momentum [GeV/c]

Beam momentum [GeV/c]CountsFigure 3.9: The beam momentum distribution of 1.69 GeV/c (a) and 1.58 GeV/c (b).

22000
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0

5

10

15

20

25

30

χ2 of K18 tracking

Figure 3.10: Typical reduced χ2 distribution of the K1.8 tracking.

68

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

3.2.5

Eﬃciency for the π + beam

The single track events were selected at this stage. The overall tracking eﬃciency of theK1.8 beam line spectrometer is expressed as
ϵK18 = ϵBC12 × ϵBC34 × ϵK18T rack ,(3.8)

where ϵBC12 and ϵBC34 are the local tracking eﬃciency of each detector, and ϵK18T rack isthe single track eﬃciency of the K1.8 global tracking. Each eﬃciency is determined as:
N (BC12T rack ≥ 1),
N (πBeam)
N (BC34T rack ≥ 1),=
N (πBeam)
N (K18T rack = 1)=,
N (BC12T rack ≥ 1 × BC34T rack ≥ 1)

ϵBC12 =

(3.9)

ϵBC34

(3.10)

ϵK18T rack

(3.11)

where N (π Beam) is the number of pions selected by BH1-BH2 time window. The overall
tracking eﬃciency of the K1.8 beam line spectrometer, ϵK18 , depends on the maximum
allowed reduced χ2 values as shown in Figure 3.11.
0.845
0.84

∈K18

0.835
0.83
0.825

χ2

0.815
0.81

< 10

BC12 and 34
χ2< 20
BC12 and 34
χ2< 30
BC12 and 34

0.82

10

20

30

40

50

60

χ2 cut value of K18 track

Figure 3.11: Summary of the ϵK18 of the χ2 cut value dependence.
The total analysis eﬃciency of beam particles is given by
ϵπ = ϵK18 × ϵBeamT OF × (1 − fµ ),(3.12)

where ϵBeamT OF is the analysis eﬃciency of time-of-flight cut between BH1 and BH2(|Beam TOF| < 2 ns) and fµ is the muon contamination in the π + beam. The contamination of muons was caused from two sources; those delivered from the upstream of themass slit and those from the π → µ decay between the QQDQQ magnet. However, theprobability of muons coming from upstream of mass slit was small compared with those3.2. ANALYSIS OF π + BEAM

69

from decay between QQDQQ magnet, which was estimated by using the Decay TURTLE
code [89]. The muons coming from decay in flight were estimated from vertical (y) distribution at BC4 position. The y distributions of the π + beam and those of decay eventswere diﬀerent according to the Decay TURTLE. Here, the reduced χ2 of the K1.8 tracking for those decay events becomes worse. The y distributions of good (χ2K18 track < 5)and bad (χ2K18 track > 30) χ2K18 track events are shown in Figure 3.12(a) and (b), respectively. The y distribution for decay events was broader than the one for π + beam
events.
×103(a): χ2K18 track < 5(b): χ2K18 track > 30(c): χ2K18 track < 30

2200

140

2000
120

1800

σ ~ 5 mm

σ ~ 16 mm

1600

100

104

10

80
60

CountsCountsCounts

1400
1200
1000

3

102

800
40

600

10

400
20
200
0
-100

-50

0

50

100

Y distribution at BC4 [mm]

0
-100

1
-50

0

50

100

Y distribution at BC4 [mm]

-100

-50

0

50

100

Y distribution at BC4 [mm]Figure 3.12: The y distribution at the BC4 position. (a) shows the one in case the χ2values are less than 5, which corresponds the y distribution of π + beam. (b) shows theone in case the χ2 values are more than 30, which corresponds the y distribution of π → µ
decay events. (c) shows the one in case the χ2 values are less than 30. This spectrum
was fitted with 2 Gaussian functions for the π + beam (red-dashed line) and the muonscomponent (blue-dashed line) to determine the fraction of muons contamination. The
total fitting functions are shown in green-solid line.

Then, we estimated the muon contamination fraction fµ by fitting the y distribution
spectra with two Gaussian functions. A fit result for the χ2K18 track cut value of 30 with
Gaussian functions for the π + beam (red-dashed line) and the muon component (bluedashed line) is shown in Figure 3.12 (c). The sum of two components is also shown witha green-solid line. The obtained fµ values are summarized in Figure 3.13.
In order to determine the χ2 cut value of each tracking, we had to consider themuon contamination fraction because it depended on the χ2K18 track cut value. Then,
we checked the analysis eﬃciency by changing the χ2 cut values and these values areplotted in Figure 3.14. The total analysis eﬃciency was the best when we chose the allof accepted χ2 values to be less than 20. Therefore, the accepted χ2 values of the local
and global tracking of the beam analysis were determined to be less than 20. In thiscut condition, the local tracking eﬃciency of BC1, 2 and BC3, 4 chambers are foundto be 93.8 ± 1.9 (syst.) % and 99.1 ± 0.1 (syst.) %, respectively. The global K1.8
tracking eﬃciency is 87.9 ± 1.2 (syst.) %. These systematic errors for the tracking are

70

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

estimated from the fluctuation of the eﬃciency during the experimental period. The
muon contamination factor was found to be 3.4 ± 0.1 (syst.) %, whose systematic error
was estimated by changing the fit method.

0.06
0.055
0.05

fµ

0.045
0.04
0.035
0.03
0.025
0.02
10

20

30

40

50

60

χ2 cut value of K18 track

Figure 3.13: A summary of fµ of χ2K18 track cut value.

0.81

χ2

0.805

∈K18 × (1 - f µ )< 10

BC12 and 34
χ2< 20
BC12 and 34
2
χ< 30
BC12 and 34

0.8
0.795
0.79
0.785
0.78

10

20

30

40

50

60

χ2 cut value of K18 track

Figure 3.14: The analysis eﬃciency of beam particles. The eﬃciency, ϵK18 × (1 − fµ ), foreach χ2 cut value are plotted in this figure.

3.3. ANALYSIS OF EMITTED K +3.3

Analysis of emitted K +3.3.1

SDC1 and SDC2 local tracking

71

The SDC1 and SDC2 were drift chambers installed at the entrance of the SKS magnet.
By using these chambers, the local straight tracking was also carried out before the SKS
global tracking.
The hit information of these chambers was obtained in the same method as BC3
and 4. However, the track through these chambers was slightly bent by the magnetic
field because the SDC2 was installed near the SKS magnet gap. Thus, the drift velocity
function was optimized in iteration not with the straight local tracking but with a helpof the SKS global tracking using the Runge-Kutta method. Furthermore, the method
to search the track candidates was diﬀerent from BC3, 4 analysis. In case of BC3, 4
analysis, we used the pair-plane analysis to resolve the L/R (left or right) because theincident angles of the beam particles were almost perpendicular. On the other hand,the emitted particles into the SKS had wide scattering angles and the incident angles on
SDC1 and 2 were not always perpendicular. Therefore, L/R was resolved from a straightpre-tracking using the same tilt angle plane (x, u, v) was performed before the straightline tracking in case of SDC1, 2 analysis. After the pre-tracking, the tracking procedureof the local tracking was same as BC3, 4 analysis.
Figure 3.15 (a) shows a typical reduced χ2 distribution of the local SDC1, 2 tracking.
The black and red histograms correspond to all the events and the single-track events,
respectively. The reduced χ2 value of less than 20 was accepted, which was determined
to keep the suﬃcient single-track eﬃciency.
The eﬃciency of SDC1, 2 (ϵSDC12 ) is the eﬃciency including the detector eﬃciency
and the analysis eﬃciency of local tracking. It was estimated from the beam trigger eventby selecting the tracks which should pass through the eﬀective area of SDC1 and SDC2
chosen from the straight track of BC3, 4 local tracking. The obtained eﬃciency was
95.7 ± 1.7 (syst.) %, whose systematic error was estimated from the hit position dependence. The fluctuation of the eﬃciency during the experimental period was suﬃciently
small compared with this error.

3.3.2

SDC3 and SDC4 local tracking

The SDC3 and SDC4 were drift chambers installed at the exit of the SKS magnet.
The drift time information was digitized by the TKO Dr.II single-hit TDC modules. The
analysis procedure of the local tracking of SDC3, 4 was same as that of SDC1, 2, although
the drift velocity function was optimized in iteration with straight local tracking. The
pre-tracking was necessary to resolve the L/R because the SDC3 and SDC4 have thesame plane structure.
Figure 3.15 (b) shows a typical reduced χ2 distribution of the local SDC3, 4 tracking.
The black and red histograms correspond to all the events and the single-track events,
respectively. χ2 value of less than 20 was accepted, which was determined to keep thesuﬃcient single-track eﬃciency. A typical residual width was 300 µm in σ.
The eﬃciency of SDC3, 4 (ϵSDC34 ) including the detector eﬃciency and local tracking
eﬃciency was obtained from the (π + , p) reaction events because proton did not decay in

72

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

104

(a)

3

10

CountsCounts

10

104

102

10

0

(b)

3

102

10

5

10

15

20

25

30

χ2 of SDC1&2 tracking

0

5

10

15

20

25

30

χ2 of SDC3&4 tracking

Figure 3.15: The reduced χ2 distribution of the SDC1, 2 (a) and SDC3, 4 (b) local
tracking. The black and red lines show the total and single-track events, respectively.

flight. It was obtained as:
ϵSDC34 =N (SDC34T rack × P roton).
N (P roton)(3.13)The proton events, N (P roton), was selected by using the information of the local tracking
in SDC1, 2 and the flight time from BH2 to TOF. Figure 3.16 shows the scatter plot
between the horizontal direction cosine (dx/dz) of the SDC1, 2 track and the flighttime (BH2-TOF). Black and red markers show all events and proton selected events,
respectively. The obtained eﬃciency was 99.2 ± 0.0 (syst.) %. The systematic error was
estimated by checking the incident angle dependence of the SDC1, 2 tracks.

Time-of-flight BH2-TOF [ns]3.3. ANALYSIS OF EMITTED K +

73

34
32

p

30
28
26
24
22

K
π

20
18
-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1 0.2

0.3 0.4 0.5

dx/dz of SDC12 track
Figure 3.16: Proton selection by the correlation of the horizontal direction cosine (dx/dz)
of the SDC1, 2 track and the time-of-flight (BH2-TOF). Black and red markers show all
events and selected proton events, respectively.

3.3.3

Momentum reconstruction of scattered particles

The momentum vector of the emitted particles was determined by reconstructing trajectories from the hit positions of SDC1–4. The Runge-Kutta method [88] was used for
track reconstruction with a magnetic filed map calculated by the ANSYS code [90]. The
trajectory and the momentum were optimized by minimizing the following reduced χ2value iteratively. The fitting parameters were the momentum, the horizontal (x) andvertical (y) positions and their direction cosines (dx/dz, dy/dz) at the TOF position.
The SKS tracking was started from the TOF position. The reduced χ2 is defined as:)n (track 2
1 ∑ xhiti − xi2
χSKS ≡,(3.14)n − 5 i=1
σiwhere n is the number of SDC layers, xhit
and σi are the hit position and positioni
track
is the estimated hit position from the track
resolution of each layer, respectively. xi
reconstruction for each layer. The convergence criterion in the iteration is δχ2 = (χ2k+1 −χ2k )/χ2k < 10−3 , where k is the number of iteration and χ2k is the tracking χ2 in the k-th
iteration.
In the present analysis, the initial parameters of x, y, u and v were obtained from the
SDC3, 4 local tracking. The initial momentum was set event by event by checking thehorizontal direction cosine (dx/dz) of the SDC3, 4 track. We set the initial momentum
which is higher about 100 MeV/c than the actual momentum as shown in Figure 3.17.
Figure 3.18 shows a typical reduced χ2 distribution of the SKS tracking. The black andred histograms correspond to all the events and kaon selected events, respectively. χ2value less than 30 was accepted, which was determined to keep the suﬃcient eﬃciency
for kaon.
The SKS tracking eﬃciency was also estimated from the (π + , p) reaction events be-

74

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

Momentum [GeV/c]

1.6
1.4
1.2
1
0.8
0.6

-0.8

-0.6

-0.4

-0.2

0

0.2

dx/dz of SDC34 track

Figure 3.17: Initial momentum function of the SKS tracking as a function of horizontal
direction cosine (dx/dz) of the SDC3, 4 track indicated with the red line. A correlation
between momenta and dx/dz of SDC3, 4 track is also shown in this figure.

104

Counts

103

102

10

1
0

5

10

15

20

25

30

35

40

45

50

χ2 of SKS tracking

Figure 3.18: Typical reduced χ2 distributions of the SKS tracking. The black and redlines indicate the distributions of total events and emitted kaon events, respectively.

3.3. ANALYSIS OF EMITTED K +75cause the emitted particles which do not decay in flight should be selected to estimate
the eﬃciency. The decay-in-flight particles such as pion make the χ2 of SKS tracking
worse. The procedure of the selection of emitted protons was same as that of SDC3, 4
in Figure 3.16.
In the present analysis, the SKS tracking eﬃciency was defined as the probability thatthe χ2 of SKS tracking was less than 30 when there were good single tracks in SDC1,
2 and SDC3, 4 local tracking. Figure 3.19 shows the eﬃciency of the SKS tracking asa function of the scattering angle (θSDC12 ), which was obtained from the local trackingof BC3, 4 and SDC1, 2. Here, the SKS tracking eﬃciency depended on the scattering
angle. Therefore, we corrected this eﬃciency event by event by checking the scattering
angle to calculate the double diﬀerential cross section.

Efficiency ( ∈SKSTrack )

0.94

0.93

0.92

0.91

0.9

2

4

6

8

10

12

14

16

θSDC12 [degree]

Figure 3.19: The SKS tracking eﬃciency as a function of scattering angle.

3.3.4

Eﬃciency for K + trigger counters

The detection eﬃciency and overkill factor of trigger counters for emitted K + (TOF,
LC, LAC) were estimated from the controlled trigger data set.
The eﬃciency of TOF and LC counter was determined from the data set of thesetriggers as
LC T riger ≡ BEAM × LC,
T OF T riger ≡ BEAM × T OF,
respectively. The hits of the estimated counters were not required in these controlled
triggers. The TOF and LC eﬃciency was obtained as:
N (T OF × T rack × LC),
N (T rack × LC)
N (LC × T rack × T OF )=,N (T rack × T OF )ϵT OF =

(3.15)

ϵLC(3.16)

76

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

where N (T rack × LC(T OF )) is the number of tracks which should pass throughthe eﬀective area of TOF (LC) selected from the local tracking of SDC3, 4 andN (T OF (LC) × T rack × LC(T OF )) the number of those tracks detected by TOF (LC).
When we estimated the LC eﬃciency, the outgoing particles were selected as π + withthe mass squared (M 2 ). The LC eﬃciency is assumed to be same for K + because thesuﬃcient yield of Čerenkov photons are obtained from K + with the momentum above the0.8 GeV/c. The eﬃciency averaged in the whole segment of TOF and LC was estimatedto be 99.5 ± 0.4 (syst.) % and 99.6 ± 0.1 (syst.) %, respectively. These systematic errors
were obtained from the diﬀerence of the eﬃciency for each segment.
The factor of LAC was estimated by considering two origins of an accidental vetofrom the π + coincidence events and a δ-ray emission from the K + as
δ –rayAcc
fLAC = fLAC
× fLAC.

(3.17)

Acc) was obtained from P IP I trigger indicated as Eq.2.6.
The accidental veto factor (fLAC
This trigger was mixed during the physics data taking as the calibration trigger and did
not required LAC anti-coincidence. In order to estimate the overkill factor, we used theemitted proton events which should not be detected by LAC and these protons wereselected in mass squared (M 2 ). The overkill factor was obtained from
Acc
fLAC
=1−

N (LAC × P roton),
N (P roton)(3.18)

where N (P roton) is the number of events at least one proton passing through the LAC
and N (LAC × P roton) is the number of accidental-hit events in LAC in the coincidence
width. The coincidence width was estimated by checking the TDC distribution of LAC
with the P IK trigger, which required the anti-coincidence of LAC. The obtained accidental veto factor was 96.3 ± 0.5 (syst.) %. The systematic error was estimated byδ –raychanging the coincidence width by ± 5 ns. The factor due to the δ-ray (fLAC) was estimated in a simulation with the Geant4 [91] and found to be 96.9 ± 0.1 (syst.) %. The
systematic error was estimated by changing the incident momenta from 0.8 to 1.2 GeV/cand the incident positions and angles in the simulation. In total, the overall factor of
LAC (fLAC ) was found to be 93.3 ± 0.5 (syst.) %.

3.3. ANALYSIS OF EMITTED K +

3.3.5

77

Kaon identification in the SKS

Time-of-flight BH2-TOF [ns]The emitted kaon was roughly selected by using the information of SDC1, 2 tracking,
TOF and LC counters. In this selection, the cuts were applied to TOF-ADC, LC-ADC
and flight-time of BH2-TOF, BH2-LC, TOF-LC. In addition, the kaon was selected using
the horizontal direction cosine (dx/dz) obtained from SDC1, 2 local tracking and theflight time between BH2 and TOF as shown in Figure 3.20. These cut regions wereloosely selected so as to keep the kaon-selection eﬃciency about 100% because the kaon
was strictly identified afterwards by a time-of-flight of BH2-TOF in combination withthe flight path length obtained from the SKS global tracking. The total kaon-selection
eﬃciency of these rough cuts was obtained to be 98.7%.

34
32

p

30
28
26

K

24

π

22
20
18

16
-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1 0.2

0.3 0.4 0.5

dx/dz of SDC12 track

Figure 3.20: Scatter plot between the horizontal direction cosine measured by SDC1, 2
and the flight time of BH2-TOF. The selected region of kaon was also indicated in the
figure.

The K + was finally identified by calculating the mass squared M 2 of the outgoingparticles as:( )2p(1 − β 2 ),M =ββ = (path length)/(flight time · c),2(3.19)(3.20)

where p and β are the momentum and the velocity of the outgoing particle, respectively.
Here, p was obtained from the SKS tracking and β was calculated from the time-of-flightand the flight path between BH2 and TOF. Figure 3.21 shows an M 2 spectrum for thedata set of the p(π + , K + ) reaction at 1.58 GeV/c (a) and the d(π + , K + ) reaction at
1.69 GeV/c (b) without any event selection by TOF and LC counters and local tracks.
The kaon selection gate was set as 0.15 < M 2 < 0.45 (GeV/c2 )2 . When there is one
good kaon track, the other tracks are discarded in the analysis.

78

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

103

Counts

102

(a)

p

π

K

10

1

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

M 2 [(GeV/c 2)2]Counts

104

(b)π

p

K

103
102

10

1
-0.2

0

0.2

0.4

0.6

0.8

1

1.2

2

M [(GeV/c 2)2]

Figure 3.21: Mass squared distributions for the outgoing particles. The M 2 distribution
without any TOF and LC cut for the data set of p(π + , K + ) at 1.58 GeV/c and d(π + , K + )at 1.69 GeV/c are shown in (a) and (b), respectively.

3.3. ANALYSIS OF EMITTED K +79

Figure 3.22 shows a mass squared (M 2 ) spectrum for the p(π + , K + )Σ+ reaction
at 1.58 GeV/c. The black and red histograms indicate the mass squared spectrum before and after the pre-selections, respectively. The kaon selected region(0.15 < M 2 < 0.45 (GeV/c2 )2 ) is shown in green arrows. The events after the
pre-selections were free from proton as observed in the red histogram. Therefore, wechose the upper limit of the M 2 to be 0.45 (GeV/c2 )2 , which was less than −5σ from theproton peak. On the other hand, there is the tail in the low M 2 region. Therefore, we
set the lower limit of the M 2 to be 0.15 (GeV/c2 )2 to avoid the contamination of pion.
It was −3σ from the kaon peak and more than +4σ from the pion peak.
The K + identification eﬃciency (ϵP ID ) was obtained asϵP ID = ϵK –Hodo × ϵP ID–M 2 ,N (M 2 cut × pre–cut)
ϵP ID–M 2 =,N (pre–cut)(3.21)(3.22)

where ϵK –Hodo is the rough cut eﬃciency using the TOF and LC. The eﬃciency for themass squared cut (ϵP ID–M 2 ) was estimated to be 98.5 ± 0.7 (syst.) %. The systematic
error was estimated by changing the pre-cut conditions. Finally, the total kaon selection
eﬃciency was estimated to be ϵP ID = 97.2 ± 0.7 (syst.) %.

p

103

Counts

2

10

π

K

10

1
-0.2

0

0.2

0.4

0.6

0.8

1

1.2

2

M [(GeV/ c2)2]
Figure 3.22: The mass square (M 2 ) distribution for the p(π + , K + )Σ+ data. The blackand red histogram are the mass square spectrum before and after the pre-selections.

80

3.4

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

Vertex reconstruction

In order to eliminate the background not coming from the target, the scattering angle
and vertex point of the (π + , K + ) reaction were reconstructed from both incident beam
and outgoing particle trajectories obtained from the BC3, 4 and SKS tracking.
Figure 3.23 shows the diﬀerence distribution of the direction cosine between the
BC3, 4 and SKS tracking measured in the beam-through data without target at
pπ+ = 0.9 GeV/c. In this figure, the horizontal (dx/dz) one and vertical (dy/dz)
one are shown in (a) and (b), respectively. We obtained the horizontal and vertical angular resolutions of 2.6 mrad and 3.3 mrad in σ, respectively. The vertical resolution was
worse than the horizontal one because of the wire configuration of the drift chamber.

800

600

500

500

400

CountsCounts

600

(a)

700

400

(b)

300

300
200
200
100

100
0
-0.03 -0.02 -0.01

0(dx/dz)K18

0.01 0.02 0.03

- (dx/dz)

SKS

0-0.03 -0.02 -0.01 0(dy/dz)K18

0.01 0.02 0.03

- (dy/dz)

SKS

Figure 3.23: The distribution of the diﬀerence of the dx/dz (a) and dy/dz (b) between
the BC3, 4 and SKS tracking. These spectra were obtained from beam-through data
without the target.

The reaction vertex was determined from the closest distance between the BC3, 4
and SKS tracks. The vertex profile of the x (horizontal) and y (vertical) direction andthe target size are shown in Figure 3.24, which was obtained from the p(π + , K + )Σ+ data
at 1.58 GeV/c. The liquid target was large enough for the incident beam with a typicalbeam size of 7.6 × 4.2 mm2 in σ.
Figure 3.26 shows the z-vertex distribution of each scattering angle (θπK ) in laboratory system. The z-vertex resolutions of each scattering angle were estimated by the
template fit as shown in red lines in Figure 3.26 and these results are summarized in Figure 3.25. These spectra were also obtained from the p(π + , K + )Σ+ data at 1.58 GeV/c.
The vertex resolution became worse for the small scattering angle. Moreover, the amountof background such as π + → µ+ decay in flight increased for the small scattering angle. Therefore, the scattering angle cut (θπK > 2◦ ) was applied. The vertex cuts in
3 direction were applied in the real target region shown by arrows.

3.4. VERTEX RECONSTRUCTION

81

50

30

40

Target sizey-vertex [mm]

30
20

25

20

10
0

15

-10
10

-20
-30

5

-40
0
-50
-50 -40 -30 -20 -10 0 10 20 30 40 50

x-vertex [mm]Figure 3.24: The vertex distribution of x and y direction, which was obtained from thep(π + , K + )Σ+ reaction data at 1.58 GeV/c. The target size is also indicated with a solidline.

z-vertex resolution [mm]

50
40
30
20
10

2

4

6

8

10

12

14

16

θπK(Lab) [deg]Figure 3.25: The summary of z-vertex resolution in each scattering angle. These values
were estimated from the fitting shown in Figure 3.26.

82

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

90 θπK < 2
80
70
60
50
40
30
20
10
0
-200
-150 -100 -50

100

4o < θπK < 6o80

CountsCounts

o

60
40
20

0

50

0
-200
-150 -100 -50

100 150 200

050

z-vertex [mm]8070

6o < θπK < 8o50

60

8o < θπK < 10o40

50CountsCounts100 150 200

z-vertex [mm]

40
30

30
20

20
10

10
0
-200
-150 -100 -50

0

50

0
-200
-150 -100 -50

100 150 200

050

z-vertex [mm]45 10 < θπK < 12
40
35
30
25
20
15
10
5
0
-200
-150 -100 -50
0oCountsCountso

50

100 150 200

z-vertex [mm]100 150 200

z-vertex [mm]20 12o < θ < 14o
πK
18
16
14
12
10
8
6
4
2
0
-200
-150 -100 -50
050

100 150 200

z-vertex [mm]Figure 3.26: The vertex distribution of z direction of each scattering angle (θπK ) inlaboratory system obtained from the p(π + , K + )Σ+ data at 1.58 GeV/c . The vertex
resolutions of z direction were estimated by the fitting as the red lines. The target size
was indicated by arrows.

3.4. VERTEX RECONSTRUCTION83

The eﬃciency of the x-vertex and y-vertex cuts were assumed to be 100%. Therefore,
only the z-vertex selection, which was selected as the target size, was considered for theestimation of the vertex cut eﬃciency. The z-vertex selection eﬃciency was determinedfrom the resolutions as shown in Figure 3.25. These eﬃciency as a function of scattering
angle are plotted in Figure 3.27. We corrected the vertex cut eﬃciency event by eventby using the scattering angle to calculate the double diﬀerential cross section.

Vertex efficiency

0.95
0.9
0.85
0.8
0.75
0.7
2

4

6

8

10

12

14

16

θπK(Lab) [deg]Figure 3.27: The vertex cut eﬃciency as a function of scattering angle. These values
were estimated from the z-vertex resolution as shown in Figure 3.25.

84

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

3.5

Momentum correction

We applied two types of momentum corrections. One is the momentum correction ofemitted K + in order to optimize the missing-mass resolution. It is because, we can see
the correlation between the missing-mass and the scattering angle of the p(π + , K + )Σ+reaction. Next, we corrected the momenta of beam pions to obtain the absolute momentum by using the beam-through and Σ+ productions data. It is necessary because
the discrepancy of about 3 MeV/c2 can be seen between the measured missing-mass ofp(π + , K + )Σ+ reaction and the PDG value [92].

3.5.1

Momentum correction of K +In the present experiment, the momenta of the outgoing particles were reconstructed byusing the calculated magnetic field map for the SKS magnet. However, this calculated
field map might not completely reproduce the real one. This eﬀect may cause somecorrelation between the momentum and the scattering angle.
1.21

1.2

1.21

(a)

1.205

MM p [GeV/c 2]

MM p [GeV/c 2]

1.205

1.195
1.19
1.185
1.18
1.175
1.17
-0.3

1.2

(b)

1.195
1.19
1.185
1.18
1.175

-0.2

-0.1

0

0.1

0.2

1.17
-0.1 -0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08 0.1

0.3

dy/dz

dx/dz
1.21

1.2

1.21

(c)

1.205

MM p [GeV/c 2]

MM p [GeV/c 2]

1.205

1.195
1.19
1.185
1.18
1.175
1.17
-0.3

1.2

(d)

1.195
1.19
1.185
1.18
1.175

-0.2

-0.1

0

0.1

0.2

0.3

dx/dz

1.17
-0.1 -0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08 0.1

dy/dz

Figure 3.28: Scatter plots between the direction cosines and the missing mass in thep(π + , K + )Σ+ reaction at 1.58 GeV/c. The figures (a) and (b) show the plot before
correction and figures (c) and (d) show the plots after correction.

Figure 3.28(a) and (b) show scatter plots between the missing mass (M Mp ) in thep(π , K + )Σ+ reaction at 1.58 GeV/c and the horizontal (dx/dz, a) or the vertical (dy/dz,b) direction cosines at the target position. This correlation was removed by introducing aphenomenological correction as the fifth order polynomial in both horizontal and vertical+3.5. MOMENTUM CORRECTION85

direction cosines. These parameters were obtained by fitting the momentum diﬀerence,measured
dpK = pcalc, as a function of dx/dz or dy/dz. The (pcalc
K − pKK ) was the calculated++++
K momentum assuming the kinematics of the p(π , K )Σ reaction and the pmeasuredK
was the measured momentum from the SKS tracking. Figures 3.28(c) and (d) show
scatter plots after this correction. This momentum correction of K + was applied to theanalysis of whole data.

Energy loss correction
The energy loss in materials was corrected in order to reconstruct the real momentum
and optimize the missing-mass resolution.
For the beam π + , the energy loss corrections in BH2 and the targets were taken
into account. These values were estimated from the π + beam-through data with andwithout target at 0.9 GeV/c. The energy loss of the target was obtained as the shiftof the centroid of the momentum diﬀerence measured from the K1.8 tracking and the
SKS tracking with and without the target in the beam-through data. The obtained sifts
for the hydrogen and deuterium target were 3.2 ± 0.1 MeV/c and 3.6 ± 0.2 MeV/c,
respectively. These values are about 10% lower than the values of Bethe-Bloch formula.
The energy loss in BH2 was corrected using the Bethe-Bloch formula by considering thisdiﬀerence.
For the emitted K + , the energy loss correction was applied with the Bethe-Blochformula. In the present analysis, the energy loss in the target was corrected event-byevent by using the vertex position.

3.5.2

Momentum correction of π + and systematic error

The momenta of beam pions were corrected with a linear function by considering theresult of the beam-through data at 0.9 GeV/c and p(π + , K + )Σ+ data at 1.58 and1.69 GeV/c in order to reduce the diﬀerences of Σ+ masses between the measured values
and the PDG value. Since the SKS magnetic field was fixed through the all data taking,the momentum of outgoing particle was not corrected in this analysis. The momentum diﬀerence between the K1.8 and SKS tracking, dp = pK18 − pSKS , was obtained
to be 1.8 ± 0.1 MeV/c from the beam-thorough data at 0.9 GeV/c and this value wasconsidered of the energy loss in BH2. In the p(π + , K + )Σ+ reaction, we obtained theΣ+ mass as a peak. However, the measured Σ+ masses had deviations from the PDG
value. The deviations, dM = (MΣmeasured− MΣP+DG ), are dM = −2.9 ± 0.1 MeV/c2 at+
pπ+ = 1.58 GeV/c and dM = −2.5 ± 0.1 MeV/c2 at pπ+ = 1.69 GeV/c. Thus, we canestimated the beam momentum deviation as:dM,(∂M/∂pπ )1=[βπ (MT arget − EK ) + pK cos θ],
M

dpπ =

(3.23)∂M∂pπ(3.24)The beam momentum deviation (dpπ ) for the beam-through and Σ+ production data
are summarized in Figure 3.29. The incident beam momentum was corrected with a

86

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

2dpπ [MeV/ c]

1
0
-1
-2
-3
-4
0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

p π [GeV/c]

Figure 3.29: The momentum diﬀerence (dpπ ) measured by the K1.8 beam line and the
SKS. A black point with error bar shows the momentum diﬀerence between the K1.8
and SKS tracking obtained from the beam-through data. Red and green points witherror bar show the momentum diﬀerence estimated from the Σ+ data analysis at 1.58
and 1.69 GeV/c, respectively. The fitting result with the linear function to obtain thecorrecting parameter is also shown with black line.

linear function as:
pcorr
K18 = 1.0077 × pK18 − 0.0087 GeV/c,(3.25)

where pcorr
K18 is the corrected beam momentum and pK18 is the measured beam momentum.
This correcting function was obtained from the fit as shown in Figure 3.29.
After the absolute momentum adjustment, the validity of the corrections was tested
in the π + p → K + Σ(1385)+ production at 1.69 GeV/c. Figure 3.30 shows the missing
mass spectrum in the Σ(1385)+ region in the p(π + , K + ) reaction at 1.69 GeV/c. A fit
result with a Lorentzian function for the Σ(1385)+ (dashed line) and three-body phasespace distributions for the ΛπK + (dotted line) and the ΣπK + (dot-dashed line) are also
shown. The Σ(1385)+ mass and width are found to be 1381.1 ± 3.6 (stat.) MeV/c2 and
42 ± 13 (stat.) MeV, respectively, which are consistent with the PDG values [92] within
the statistical errors.
The dpπ and dpK values after correction are summarized in Figure 3.31, where dpK
is defined as:
dM,(∂M/∂pK )1= − [βK (MT arget + Eπ ) − pπ cos θ].
M

dpK =

(3.26)∂M∂pK(3.27)

Finally, the systematic uncertainty of the momentum scale was estimated to be
1.1 MeV/c from these values.

d 2σ/d Ω/dM 2o-16o(Lab) [µb/sr/(4 MeV/c2)]

3.5. MOMENTUM CORRECTION
7
6
5

87

data
total
+
+
π+p → K Σ(1385)+
π+p → K Λπ
π+p → K+Σπ

4
3
2
1
1.25

1.3

1.35

1.4
1.45
MM p [GeV/c2]

Figure 3.30: The missing-mass spectrum of the p(π + , K + ) reaction in the Σ+ (1385) mass
region. The experimental data are shown by black points with statistical errors. The
spectrum was fitted with Σ(1385)+ (dashed line), Λπ (dotted line) and Σπ (dot-dashedline) productions. Taken from Ref. [93].

4

(a)

(b)

12
10

2

dp [MeV/c ]-2Kdpπ [MeV/c ]

8
0

-4
-6

6
4
2
0
-2

-8
-4
-10
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0.90.95 1 1.051.11.151.21.251.3

p π [GeV/c ]p [GeV/c ]K

Figure 3.31: The momentum diﬀerence after the correction. The obtained values for the
beam pions and emitted kaons are shown in (a) and (b), respectively. Black points witherror bars show the momentum diﬀerence obtained from the beam-through data. Red
and green points with error bars show the momentum diﬀerence estimated from the Σ+data analysis at 1.58 and 1.69 GeV/c, respectively. Blue points with error bars show thevalues estimated from the Σ(1385)+ data analysis at 1.69 GeV/c.

88

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

3.6

Missing-mass resolution

In this subsection, we discuss a missing-mass resolution. The goal of this part is toestimate the missing-mass resolution of the d(π + , K + ) reaction by using the informationof the beam-through and p(π + , K + )Σ+ data. The missing mass resolution (∆M ) was
estimated from:∆M 2 = ∆2K18 + ∆2SKS + ∆2θ + ∆ET2 arget .
(3.28)
Then, the missing-mass resolution can be divided to the contributions of the resolutionsof K1.8 beam line spectrometer (∆K18 ), the SKS (∆SKS ) and scattering angle (∆θ ) andthe energy loss straggling in the target (∆ET arget ). Further, each term in the equation
can be expressed as:
∂M 2
∂M 2
∂M 2 2) ∆pK18 2 + () ∆pSKS 2 + () ∆θ + ∆ET2 arget , (3.29)
∂pK18
∂pSKS
∂θ
1
=
[βπ (MT arget − EK ) + pK cos θ],M1= − [βK (MT arget + Eπ ) − pπ cos θ],
M
pπ pK
= −
sin θ,
M∆M 2 = (
∂M
∂pK18
∂M
∂pSKS
∂M
∂θ

where Eπ and pπ are the total energy and momentum of pions, EK and pK are thoseof kaons, MT arget is the rest mass of the target nucleus, and θ is the scattering angleof the reaction, ∆pK18 and ∆pSKS the momentum resolution of the K1.8 beam line
spectrometer and the SKS, respectively, and ∆θ the resolution of the scattering angle.
Now, we estimate the resolution of each term. The resolution of the scattering angle
was estimated from the resolution of horizontal direction cosines (∆uK18 , ∆uSKS ) andvertical direction cosines (∆vK18 , ∆vSKS ) as
∂θ 2
∂θ 2
∂θ 2
∂θ 2
) ∆uK18 2 + () ∆uSKS 2 + () ∆vK18 2 + () ∆vSKS 2 ,
∂uK18
∂uSKS
∂vK18
∂vSKS
(
)
uK18 uSKS + vK18 vSKS + 1√
θ = arccos √ 2,
22
uK18 + vK18
+ 1 + u2SKS + vSKS
+1∆θ2 = (

where uX and vX are the direction cosines of each spectrometer.
The total resolution
√
2
2
of
the
horizontal
andverticalones
weremeasured
to
be
u
+
u
K18
SKS = 2.6 mrad and√22
vK18 + vSKS = 3.3 mrad in σ as described in Sec. 3.4. Further, the ratio of the distanceof BC3, 4 and SDC1, 2 was about 10 : 7. Thus, each angular resolution was estimatedto be (∆uK18 , ∆uSKS , ∆vK18 , ∆vSKS ) = (1.5, 2.2, 1.9, 2.7) mrad by combining theseinformation.
The energy loss term ∆ET arget was estimated by the Geant4 [91] based Monte Carlosimulation. In this simulation, not only the energy loss straggling but also the diﬀerenceof the path length in the target were included. The ∆ET arget values for three diﬀerent
kinematics: the Σ+ production at 1.58 GeV/c, the K − pp production and the ΣN cusp,
were obtained to be 0.6 MeV, 0.8 MeV and 0.8 MeV, respectively.

3.6. MISSING-MASS RESOLUTION

89

Table 3.3: The scattering-angle resolutions and the missing mass resolutions of the Σ+
production at 1.58 GeV/c data.
θ [degree]
2–4
4–6
6–8
8–10
10–12
∆θ [mrad] (FWHM)
6.9±0.5 6.7±0.5 6.4±0.3 6.3±0.1 6.2±0.1
2+∆MΣ [MeV/c ] (FWHM) 2.5±0.1 2.5±0.1 2.7±0.1 2.7±0.1 2.7±0.2
Total momentum resolution of the K1.8 beam line spectrometer and the SKS
was estimated from the beam-through data without a target. The total resolution,∆p2beam-through = ∆p2K18 + ∆p2SKS , was obtained from the width of the momentum diﬀerence measured from K1.8 tracking and the SKS tracking to be 2.2 MeV/c. Furthermore,
we have information of the missing-mass resolution of the p(π + , K + )Σ+ reaction. The
measured missing-mass resolution of Σ+ for each scattering angle is listed in Table. 3.3.
Here, the resolution of the scattering angle in the p(π + , K + )Σ+ kinematics for each angle
was calculated by using the measured direction cosines event by event. These angularresolutions for the Σ+ kinematics were also listed in Table. 3.3. Thus, we can estimate
the momentum resolution of K1.8 beam line spectrometer (∆pK18 ) and the SKS (∆pSKS )by solving the Eq. 3.29 for the kinematics of p(π + , K + )Σ+ reaction with the informationof ∆pbeam-through and ∆θ (in Table. 3.3). The momentum resolution of each spectrometer
calculated in this scheme is summarized in Figure 3.32. The solid and dashed lines in thisfigure show the mean value and root mean square, respectively. Therefore, we estimatedthe resolutions of all components of Eq. 3.29. Finally, by using those resolutions, themissing mass resolution of d(π + , K + ) reaction for two diﬀerent kinematics: the K − pp
(2.27 GeV/c2 ) and the ΣN cusp (2.13 GeV/c2 ), were estimated to be 2.7 ± 0.1 MeV/c2
and 3.2 ± 0.2 MeV/c2 , respectively.

0.24

0.24
0.22

0.2

∆p/p %(FWHM)∆p/p %(FWHM)

0.22

(a)

0.18
0.16
0.14

0.2
0.18
0.16
0.14

0.12

0.12

0.1

0.1

0.08

2

4

6

8

10

12

θπK [degree]

(b)

0.08

2

4

6

8

10

12

θπK [degree]

Figure 3.32: The momentum resolution of K1.8 beam line spectrometer (a) and the
SKS (b). The solid and dashed lines are mean values and root mean squares, respectively.

90

3.7

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

Cross section

After selecting the (π + , K + ) events, the missing-mass spectrum was obtained as a double
diﬀerential cross section of d2 σ̄θ1 –θ2 /dΩ/dM averaged over the scattering angle from θ1
to θ2 . The double diﬀerential cross section is calculated as:
d2 σ̄θ1 –θ2
A
NπK
=
,
dΩdM
NA (ρx) Nbeam ∆Ωθ1 –θ2 ∆M ϵ

(3.30)

ϵ = ϵπ × ϵK × ϵDAQ × ϵtrig × ϵvertex ,ϵπ = ϵBeamT OF × (1 − fµ ) × ϵBC12 × ϵBC34 × ϵK18T rack ,ϵK = ϵT OF × ϵLC × fLAC × ϵSDC12 × ϵSDC34 × ϵSKST rack × ϵP ID × fdecay ,where A is the target mass number, NA the Avogadro constant, ρx the target mass
thickness, NπK the number of good (π + , K + ) events in the missing-mass interval ∆M ,Nbeam the number of beam pions on the target, ∆Ωθ1 –θ2 the solid angle of SKS between
θ1 and θ2 and ϵ the overall experimental eﬃciency resulting from DAQ, detectors, andanalysis cuts including the K + decay factor. The experimental eﬃciency except for
DAQ (ϵDAQ ), the trigger bias (ϵtrig ), K + decay factor and acceptance of the SKS isalready described in previous sections in this chapter. A typical value of the overall
experimental eﬃciency is ϵ = 17.6±0.7 (syst.) %. In this section, we describe proceduresof the estimation of these remaining eﬃciency.

3.7.1

Data acquisition eﬃciency (ϵDAQ )The data acquisition eﬃciency, ϵDAQ , caused by the dead time of the data acquisition
system, was obtained as a probability that 1st-level trigger is accepted when the dataacquisition system generates triggers. ϵDAQ was obtained as a function of the triggerrate, and the typical value was 65.7 ± 1.0 (syst.) %. The main contribution of the deadtime was the data transfer time of the TKO multi-hit TDC module.

3.7.2

Eﬃciency of the trigger bias (ϵtrig )During the d(π + , K + ) data taking, the pre-scaled unbiased (π, K) trigger data without
the matrix trigger, the mass trigger and BVH anti-coincidence was also taken withthe pre-scaled factor of 100. Then, these trigger eﬃciency and accidental veto factor
was determined by comparing the (π, K) inclusive trigger data and the unbiased (π, K)
trigger data. Figure 3.33 shows the obtained missing mass (M Md ) spectra in each trigger
condition. In this figure, the unbiased (π, K) trigger data was scaled by considering the
pre-scaled factor and the diﬀerence of ϵDAQ in each trigger condition. Here, we checked
the overall missing mass structure were consistent with each other. Finally, the overall
eﬃciency of these trigger was evaluated by diving those spectra as shown in Figure 3.34.
These values were averaged in whole M Md region to be 91.6 ± 0.7 (syst.) %, whose
systematic error was estimated from the diﬀerence in each M Md region.

Counts

3.7. CROSS SECTION

91

40000

unbiased (π, K) trigger

30000(π, K) inclusive trigger

20000

10000

0

2.1

2.2

2.3

2.4

MM d [GeV/c2]
Figure 3.33: Comparison between (π, K) inclusive trigger data (black points) and theunbiased (π, K) trigger data (red points).

1

Efficiency

0.95

0.9

0.85

0.8

2.1

2.2

2.3

2.4

2.5

MM d [GeV/c2]

Figure 3.34: Eﬃciency of the Matrix trigger, Mass trigger and BVH accidental vetofactor as a function of M Md .

92

3.7.3

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

K + decay factor (fdecay )A part of K + produced in the target decayed in flight in the SKS magnet. Since thedecay products such as µ+ could be detected, the kaons which decayed before passing
through the LAC were rejected in the trigger level. The survival rate until the LAC,
fdecay , was estimated event by event as a function of the flight path length (LK ) of thekaons and its βγcτ as:
fdecay = exp(−LK /βγcτ ),(3.31)
where τ was life time of K + . The obtained decay factor as a function of missing
mass (M Md ) of the d(π + , K + ) data was shown in Figure 3.35. A typical value was
58.8 ± 0.3 (syst.) %. The systematic error was estimated by taking into account theradiator size of LAC.

Decay factor [%]

100
80
60
40
20
0
2

2.1

2.2

2.3

2.4

2.5

MM d [GeV/c2]

Figure 3.35: The obtained decay factor as a function of M Md .

3.7. CROSS SECTION

3.7.4

93

Acceptance of the SKS

The eﬀective solid angle of the SKS (∆Ωθ1–θ2 ) was estimated with a Monte Carlosimulation based on the Geant4 [91]. The solid angle with the missing mass (M Md or
M Mp ) and the scattering angle (θ) is defined as:∫ θ2
d cos(θ) × ϵAcc ,(3.32)N (accepted events),
N (generated events)(3.33)∆Ωθ1–θ2 (M M, θ) = 2πθ1ϵAcc =

where θ1 and θ2 are expressed as θ − 12 ∆θ and θ + 12 ∆θ using a fixed interval (∆θ).
In the event generation, the beam profiles of (xb , yb , (dx/dz)b ,(dy/dz)b , pb ) were produced from the experimental data, where xb , yb , (dx/dz)b ,(dy/dz)b , pb are the horizontal
and vertical position and their direction cosines and the momentum of a beam particle
at the target, respectively. The distribution in the z-direction is generated assuming aflat distribution.
The scattered kaons were generated assuming the π + + d (p) → K + + X reaction.
Then, we checked the mass of X in this reaction with missing mass and the scattering
angle event by event. The obtained table of the ϵAcc in Eq. 3.32 as a function of themissing mass and the scattering angle is shown in Figure 3.36 for the deuteron target dataand in Figure 3.37 for the proton target data. The incident momentum is 1.69 GeV/c inboth cases.
In the simulation, the multiple-scattering eﬀect, the energy loss and the hadronicinteraction were taken into account. In the present analysis, a mesh size of the table is
2 MeV/c2 in the missing mass axis and 0.1 degrees in the scattering angle axis.
In the present analysis, the upper limit of the M Md (M Mp ) was set to be 2.47 GeV/c2(1.44 GeV/c2 ) because the SKS acceptance was small and changed rapidly in these large
M Md and M Mp regions. Moreover, we selected events in the scattering angle from 2◦
to 16◦ for the same reason.

94

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

2.5
0.9
0.8

MM d [GeV/c2]

2.4

0.7

2.3

0.6
0.5

2.2

0.4
0.3

2.1

0.2
0.1

2
0

2

4

6

8

10

12

14

16

18

20

0

θπK(Lab) [degree]

Figure 3.36: The acceptance table for the d(π + , K + ) at 1.69 GeV/c data.

0.9

1.4

MM p [GeV/c2]

0.8
0.7

1.3

0.6
0.5

1.2

0.4
0.3

1.1

0.2
0.1

1
0

2

4

6

8

10

12

14

16

18

20

0

θπK(Lab) [degree]

Figure 3.37: The acceptance table for the p(π + , K + ) at 1.69 GeV/c data.

3.7. CROSS SECTION

95

Table 3.4: The list of the experimental eﬃciency and systematic error for the common
factor (ϵcom ).
Factors
ϵBeamT OF
1 − fµϵBC12
ϵBC34
ϵK18T rack
ϵT OF
ϵLC
fLAC
ϵSDC12
ϵSDC34
ϵP ID
ϵDAQ
ϵtrig

3.7.5

Meaning
Beam TOF eﬃciencyµ contamination factor
BC1-2 eﬃciency
BC3-4 eﬃciency
K1.8 tracking eﬃciency
TOF eﬃciency
LC eﬃciency
LAC factor
SDC1-2 eﬃciency
SDC3-4 eﬃciency
PID eﬃciency for K+
Data-acquisition eﬃciency
Trigger eﬃciency (Matrix, Mass, BVH)
Total

Typical value (ϵ) [%]99.6 ± 0.1
96.6 ± 0.1
93.8 ± 1.9
99.1 ± 0.1
87.9 ± 1.2
99.5 ± 0.4
99.6 ± 0.1
93.3 ± 0.5
95.7 ± 1.7
99.2 ± 0.0
97.2 ± 0.7
65.7 ± 1.0
91.6 ± 0.7
ϵcom = 40.4 ± 1.5∆ϵ/ϵ [%]
0.1
0.1
2.0
0.1
1.4
0.4
0.1
0.5
1.8
0.0
0.7
1.5
0.8
3.6

Systematic errors

There were two kinds of eﬃciency and factors in Eq. 3.30. One is the eﬃciency corrected event by event. It includes the SKS tracking eﬃciency (ϵSKST rack ), the decay
factor (fdecay ), the vertex eﬃciency (ϵvertex ) and the acceptance of SKS (ϵAcc ). The othereﬃciency is common to all events. These common eﬃciency with systematic errors are
summarized in Table 3.4 and found to be ϵcom = 40.4 ± 1.5 (syst.) %. The totaleﬃciency, ϵ, is described asϵ = ϵcom × ϵSKST rack × ϵdecay × ϵvertex × ϵAcc .

(3.34)The errors of eﬃciency corrected event by event are shown in Figure 3.38, whose
errors were averaged in all events for each missing mass bin. Here, the error of ϵAcc wasestimated by changing the mesh size of the acceptance table as (1, 2, 3) MeV/c2 for the
missing-mass mesh and (0.05, 0.1, 0.15) degrees for the scattering-angle mesh.
The total systematic error of correcting factors, ϵ, in Eq. 3.30, are shown in Figure 3.39
as a function of missing mass. The fluctuation of the systematic error in each missingmass bin is small and the averaged value is ∆ϵ/ϵ = 4.4%.

96

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS(b): f decay
3

2.5

2.5

∆ f decay/ f decay [%]∆ ∈SKSTrack / ∈SKSTrack [%](a): ∈SKSTrack
3

2
1.5
1
0.5
0

2.1

2.2

2.3

1.5
1
0.5
0

2.4

MM d

2

2.1

2.2

(c): ∈vertex(d): ∈Acc
3

2.5

2.5

∆ ∈Acc / ∈Acc [%]∆ ∈vertex / ∈vertex [%]2.4

MM d [GeV/c 2]

3

2
1.5
1
0.5
0

2.3

[GeV/c 2]

2
1.5
1
0.5

2.1

2.2

2.3

0

2.4

MM d

2.1

2.2

[GeV/c 2]

2.3

2.4

MM d [GeV/c 2]

Figure 3.38: The systematic error of the ϵSKST rack , fdecay , ϵvertex and ϵAcc as functions of
missing-mass for the d(π + K + ) at 1.69 GeV/c data.

Systematic error ∆∈/∈ [%]

8
7
6
5
4
3
2
1
0

2.1

2.2

2.3

2.4

MM d [GeV/c2]

Figure 3.39: The total systematic error (∆ϵ/ϵ) for the double diﬀerential cross section
as a function of missing-mass.

3.8. THE Σ+ PRODUCTION CROSS SECTION

3.8

97

The Σ+ production cross section

In order to check the overall validity of the eﬃciency correction, we compared the differential cross sections of the p(π + , K + )Σ+ reaction between our measurement and oldmeasurement at the same momenta of 1.58 and 1.69 GeV/c by Candlin et al. [94]. Figure 3.40 shows the missing-mass spectrum (M Mp ) obtained from the incident beam
momenta of 1.58 (1.69) GeV/c in (a)((b)). Thus, the Σ+ peaks were clearly observed.

(a)

500
400
300
200
100
0
1.17

(b)

600

Counts [/(0.5MeV/c2]

Counts [/(0.5MeV/c2]

600

500
400
300
200
100

1.18

1.19

1.2

1.21

MM p [GeV/c2]

0
1.17

1.18

1.19

1.2

1.21

MM p [GeV/c2]

Figure 3.40: The obtained missing-mass spectra (M Mp ) for the p(π + , K + )Σ+ . The
spectra of the incident beam momenta of 1.58 GeV/c and 1.69 GeV/c are shown in (a)and (b), respectively.

Figure 3.41 shows the three kinematical lines as a function of particle momentum
and scattering angle for the p(π + , K + )Σ+ reactions at 1.58 GeV/c (solid line) and1.69 GeV/c (dashed line) and the d(π + , K + )K − pp reaction at 1.69 GeV/c assuming
the binding energy of 100MeV (dotted line). The acceptance of the SKS is also shown inthis figure. The kinematical line of the Σ+ production reaction at 1.58 GeV/c and thed(π + , K + )K − pp have a good overlap with the almost flat momentum acceptance region.
As shown in Figure 3.41, the kinematical lines of the Σ+ productions at two diﬀerent
incident momenta run through diﬀerent acceptance ares. In both cases, we obtained areasonable agreement between our data and the previous ones within the large errors
as shown in Figure 3.42 for 1.58 GeV/c and Figure 3.43 for 1.69 GeV/c. Since the oldmeasurement was given in the center of mass system, these were transformed to thelaboratory system for comparison.

CHAPTER 3. ANALYSIS I - INCLUSIVE ANALYSIS

K+ momentum (Lab) [GeV/c ]

98

1.6

1

1.5

0.9

1.4

0.8
0.7

1.3

0.6

1.2
0.5

1.1
0.4

1

0.3

0.9

0.2

0.8

0.1

0.7
0

2

4

6

8

10 12 14 16 18 20
Scattering Angle θπK(Lab) [degree]0

Figure 3.41: Three kinematical lines of K + for the p(π + , K + )Σ+ reactions at
1.58 GeV/c (solid line) and 1.69 GeV/c (dashed line) and the d(π + , K + )K − pp reaction at 1.69 GeV/c assuming the binding energy of 100MeV (dotted line). Acceptanceof the SKS is also shown. Taken from Ref. [93].

3.8. THE Σ+ PRODUCTION CROSS SECTION

99

800

d σ/d ΩLab [µb/sr]

700
600
500
400
300

Present data200

Old data

100
0

2

4

6
8 10 12 14 16
Scattering Angle θπK(Lab) [degree]

Figure 3.42: The diﬀerential cross section of Σ+ production at pπ+ = 1.58 GeV/c. The
present data and the referenced old ones [94] are shown by crosses with statistical errors
and open circles, respectively.

800

d σ/d ΩLab [µb/sr]

700
600
500
400
300

Present data200

Old data

100
0

2

4

6
8 10 12 14 16
Scattering Angle θπK(Lab) [degree]

Figure 3.43: The diﬀerential cross section of Σ+ production at pπ+ = 1.69 GeV/c. The
present data and the referenced old ones [94] are shown by crosses with statistical errors
and open circles, respectively. Taken from Ref. [93].

Chapter 4
Analysis II - Coincidence analysis
The analysis for RCA is discussed in this chapter. The goal of this part is to select the
proton by using the information of RCA and determine the momentum of proton.

4.1

Outline

The RCA was composed of six segments of range counter array and each segment had
five layers plastic scintillation counters, where the first two layers were segmented into
two slabs. Every scintillation counter was read out from both up and down sides byphototubes (PMT). Thus, the RCA had total 84 PMT’s and we read out the ADC and
TDC information from every PMT. Each segment of RCA is analyzed with the sameprocedures.
In the RCA analysis, we measured the velocity (β) to determine the proton momentum as β = (path length)/(TOF·c), where the path length was measured from the(π + , K + ) vertex position and hit position on the first layer of RCA obtained from thetime diﬀerence between the up and down PMT’s, TOF was the time of flight between
the BH2 and the first layer of RCA and c is the light velocity. The particle identification(proton selection) was carried out by using the particle identification parameter (P ID),
which was calculated using the information of the energy deposit, the velocity and stopping layer. Thus, the energy deposit information was used to obtain not the kinetic
energy of the incident particles but the P ID because the velocity had less uncertainties
than the total energy deposit.
The analysis is carried out as the following procedures:• The velocity of each particle was reconstructed by combining the information of TOF and the path length. TOF was measured from the time difference between BH2 and the first layer of RCA, whose time oﬀset parameters were adjusted by using the π + (β ∼ 1) from the Σ+ → π + n decay in the π + d √→ K + Σ+ X reaction. The path length was determined as(xRCA − xπK )2 + (yRCA − yπK )2 + (zRCA − zπK )2 , where (xπK ,(path length) =yπK , zπK ) were the (π + , K + ) vertex positions and (xRCA , yRCA , zRCA ) were the hit
positions in the first layer of RCA.
• The energy gain of each layer of RCA was calibrated by using the information
1004.2. VELOCITY CALIBRATION

101

of the pedestal and the pulse height for minimum ionization particles (MIP) andstopped proton events in the RCA. The particle identification parameter (P ID)
was set up from the energy deposit of each layer. The gain adjustment is important
to correctly calculate the P ID.
• Proton was selected by combining the information of the stopping layer of RCA,
the velocity and the P ID. The momentum of the proton was reconstructed fromthe velocity and the hit position of the first layer of RCA.

4.2

Velocity calibration

Velocity of a particle (β) was obtained as β = (path length)/(TOF·c), where c was thelight speed. TOF was the time-of-flight for each particle obtained from the hit timingsof BH2 and the first layer of RCA.
The TDC values of these counters were converted to the time using the TDC conversion gain. A slewing correction was carried out to improve the time resolution. In
this analysis, the parameters of this correction for BH2 were determined by using thebeam π + . In case of RCA, these parameters were tuned by using the information of thefirst and second layers in order to reduce the ambiguity of the flight path length. In thisdetermination of the parameters, the high velocity (β ∼ 1) and the small energy loss
events corresponding to the MIP were selected for all layers of RCA. Figures 4.1 and 4.2
show a typical scatter plot between the ADC and flight time before/after the slewing
correction for the BH2 and RCA, respectively. After this correction, the time resolutionof the TOFBH2−RCA was found to be 158 ± 16 ps.
The path length was obtained as,√(path length) =(xRCA − xπK )2 + (yRCA − yπK )2 + (zRCA − zπK )2 ,(4.1)
where (xπK , yπK , zπK ) was vertex position of the (π + , K + ) reaction and (xRCA , yRCA ,zRCA ) was the hit position in the first layer. In this analysis, the horizontal hit position (xRCA and zRCA ) was assumed to be the center of the scintillators and the vertical
hit position (yRCA ) was obtained from the time diﬀerence between the up and down
PMT’s. The light velocity inside the scintillators was measured to be 14.4 ± 1.0 cm/ns
by using the cosmic rays by changing the relative position defined by the small trigger
counters. Thus, the vertical position resolution of RCA was about 8 mm. The time oﬀset
between the up and down PMT’s corresponding to the center of the vertical position wasdetermined by fitting the time diﬀerence spectrum with a Gaussian function as shownin Figure 4.3.
The time oﬀset for each segment of RCA was properly adjusted by using the π +peak from the Σ+ decay of the π + d → K + Σ+ ns reaction, where ns was the spectator
neutron, by selecting the missing-mass (M Md ) region of 2.15 < M Md < 2.22 GeV/c2(see Figure 5.1). Figure 4.4 shows a typical obtained 1/β spectrum of this missing-mass
region compared with the simulated one. In this comparison, a small energy-loss events
corresponding to the MIP were selected to reject the other particles such as a proton
from the Σ+ decay. The accuracy of this time-oﬀset adjustment was better than 100 ps,
which was studied by using two-proton coincidence events described in Appendix B.

102

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS(a): Before correction
3.5(b): After correction
450

3.5

400

300
250

2.5

200
150

2

100

[ns]
BH1-BH2

3

Flight time

Flight time

BH1-BH2

[ns]

400
350

350

3

300
250

2.5
200
150

2

100

50

1.5
200 220 240 260 280 300 320 340 360 380 400

50

1.5
200 220 240 260 280 300 320 340 360 380 400

0ADC BH2 seg 4 (up) [ch]0

ADC BH2 seg 4 (up) [ch](c): Before correction(d): After correction

3.5

3.5

400

250

2.5

200
150

2

100

[ns]
BH1-BH2300

3Flight time

Flight time

BH1-BH2

[ns]

350
350

3

300
250

2.5

200
150

2

100

50

1.5
180 200 220 240 260 280 300 320 340 360

50

1.5
180 200 220 240 260 280 300 320 340 360

0ADC BH2 seg 4 (down) [ch]0

ADC BH2 seg 4 (down) [ch]Figure 4.1: A typical scatter plot between the ADC of up and down PMT’s of BH2 andflight time of BH1 to BH2. The scatter plot before the slewing correction are shown in(a): (ADC of up PMT) and (c): (ADC of down PMT). Similarly, the scatter plot after
the slewing correction in (b) and (d).

(b): After correction

10

5

8

4.5

6

4

4

3.5

2

3

0

200 250 300 350 400 450 500 550 600

[ns]

5.5

(RCA) 1st layer - 2nd layer

12

Flight time

Flight time(RCA) 1st layer - 2nd layer[ns](a): Before correction
6

6

10

4.5

6
4

3.5
2

3

200 250 300 350 400 450 500 550 6000(d): After correction

10

5

8

4.5

6

4

4

3.5

2

0

[ns]

5.5

(RCA) 1st layer - 2nd layer

12

Flight time[ns](RCA) 1st layer - 2nd layer

Flight time84(c): Before correction

ADC in the 1st layer of RCA (down) [ch]12

ADC in the 1st layer of RCA (up) [ch]6

200 250 300 350 400 450 500 550 600

145ADC in the 1st layer of RCA (up) [ch]

3

16

5.5

6

18
16

5.5

14

5

12
10

4.5

8

4

6
4

3.5

2

3

200 250 300 350 400 450 500 550 600

0ADC in the 1st layer of RCA (down) [ch]Figure 4.2: A typical scatter plot between the ADC of up and down PMT’s of the firstlayer of RCA and flight time of the first layer to second layer of RCA. The scatter plot
before the slewing correction are shown in (a): (ADC of up PMT) and (c): (ADC ofdown PMT). Similarly, the scatter plot after the slewing correction in (b) and (d).

4.2. VELOCITY CALIBRATION

103

700
600
Counts

500
400
300
200
100
0

-10

-8

-6

-4

-2

0
2
4
6
TDC down - TDC up [ns]Figure 4.3: A typical time diﬀerence spectrum between the up and down PMT’s of thefirst layer of RCA before the adjustment. The spectrum was fitted with a Gaussianfunction (red line) to obtain the time oﬀset corresponding to the center of the vertical
position of RCA.

160

data
simulation+
π+ d → Σ+ K ns
Σ+ → π+ n140Counts

120
100
80
60
40
20
0
0

0.5

1

1.5

2

2.5

3

3.5

4

1/β

Figure 4.4: A typical 1/β spectrum around the quasi-free Σ production region of thed(π + , K + ) reaction compared with simulation. In this figure, the π + event from the Σ+
decay was selected by requiring the small energy loss events.

104

4.3

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS

Gain calibration

ADC in the 4th layer [ch (nom)]

A light output of plastic scintillator is not necessarily proportional to the energy deposit
because the light output tends to be saturated as the energy deposit becomes larger
due to the quenching eﬀect [95]. Thus, the relative gain of each PMT was corrected byusing the ADC pedestal information and the peak pulse heights for MIP and for stopped
proton events in the RCA, and fitted with a second order polynomial.
As the first step, we roughly adjusted the ADC value (ch) of each counter with a linear
function by using two peaks corresponding to the pedestal and MIP. In the selection of
the MIP event, the high velocity β ∼ 1 and the vertical hit position around the center
were chosen in order to reduce the ambiguity of the incident angle.

7
6
5

p

4

π

3
2
1
0
0

1

2

3

4

5

6

7

8

9

10

ADC in the 3rd layer [ch (nom)]

Figure 4.5: The correlation plot between the normalized ADC values of the third layer
and fourth layer of RCA. We can see the stopped charged pion’s and proton’s clusters
as shown in blue and red lines, respectively.

From the hit pattern of five layers, we can define the stopping layer, istop , for each
RCA. Figure 4.5 shows a typical correlation plot between the normalized ADC valuesof the third layer and fourth layer of RCA for the events of istop = 4. In this figure,
we can see the charged pion’s and proton’s clusters stopping at the fourth layer of RCA
as shown in blue and red lines, respectively. Then, we obtained the maximum energy
deposit for these proton events stopping at the forth layer by fitting with a functiona{d + tanh(b(−x + c))} as shown in Figure 4.6 (a). In this proton selection, theof 1+dvertical hit position around the center (< ± 10 cm) was also chosen in order to select theperpendicular incident events. The same fitting procedure was applied to the simulated
one constructed with Geant4 program [91], as shown in Figure 4.6 (b). The energy
deposit at this maximum ADC channel was adjusted with the simulation value in MeV.
We could also obtain the maximum energy deposit of stopping protons in the otherlayers. Figure 4.7 (a) shows an obtained normalized ADC spectrum of the second layerof RCA for the proton events stopping at the fourth layer. The maximum value for4.3. GAIN CALIBRATION

105(a): Data(b): Simulation

400

250

350
200

CountsCounts

300
250
200

150
100

150
100

50

50
0
0

2

4

6

8

10

0
0 10 20 30 40 50 60 70 80 90 100

12ADC in the 4th layer [ch (nom)]dE in the 4th layer [MeV]

Figure 4.6: The obtained normalized ADC (a) and simulated energy deposit (b) spectraof the fourth layer of RCA for the stopping proton at this layer. The maximum energyadeposit of this proton was found by fitting with the function of 1+d{d + tanh(b(−x + c))}as shown in red lines.

these events was also obtained by fitting with the same function in Figure 4.6. The
same fitting procedure was also tested for the simulated one as shown in Figure 4.7 (b).
However, the maximum energy deposit of stopping proton was sometimes not clear. For
instance, the maximum energy deposit in the second layer, where proton stopped in thethird layer, was not clear. Thus, we did not take into account these unclear conditions
for the energy correction.
(a): Data(b): Simulation
250

800
700

200

CountsCounts

600
500
400

150
100

300
200

50

100
0
0

2

4

6

8

10

12

ADC in the 2nd layer [ch (nom)]00

5 10 15 20 25 30 35 40 45 50

dE in the 2nd layer [MeV]

Figure 4.7: The obtained normalized ADC (a) and simulated energy deposit (b) spectraof the second layer of RCA for the stopping proton at the fourth layer. The maximum
energy deposit of this proton was found by fitting with the same function of Figure 4.7
as shown in red lines.

106

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS

Finally, the normalized ADC value of each layer was converted to the energy depositby fitting with a second order polynomial. We show a case for the second and fourth layer
in Figure 4.8. Here, we used the information of the penetrate events for this correction
for small energy deposit region such as MIP. Therefore, we could not correct the ADC
values validly for the particles stopping in this layer for the small energy loss events,
although we corrected the ADC values validly for the penetrate particles.
(a)

90
80

40

30
pedestal
MIP
stop4 (p)stop2 (p)

20
10

0
0

2

4
6
8
10
12
ADC 2nd layer of RCA [ch(norm)]dE 4th layer of RCA [MeV]dE 2nd layer of RCA [MeV]

50

(b)

70
60
50
40
pedestal
MIP
stop4 (p)

30
20
10
0
0

1

2

3
4
5
6
7
ADC 4th layer of RCA [ch(norm)]

Figure 4.8: A typical correlation between the normalized ADC values and the energy
deposits fitted with a second order polynomial indicated with the black lines for thesecond and fourth layer of RCA shown in (a) and (b), respectively.

4.3.1

P ID parameter

In order to carry out the particle identification, we set up the particle identification
parameter, P ID, as()
f istop + dE
f (i −1) )α − (dEf istop )α · cos θ,
P ID = (dE
(4.2)
stop
f istop and dE
f istop −1 shows the energy deposit in the stopping layer, istop , andwhere dE
previous layer of the stopping one, respectively. The θ is the incident angle for RCA.
The α is a constant parameter, whose typical value was 1.75. The P ID corresponds
to the thickness of the previous layer of the stopping one and it should depend on not
momentum but charge number and mass of the particle1 .
Figure 4.9 shows a typical scatter plot between the energy deposit of the second
layer and P ID, where the α was set at 1.58 (a) and 1.73 (b), for the istop = 2 events.
The parameter α was adjusted for each counter by fitting the P ID for protons so as
to have the minimum width (χ2 ). Figure 4.9 with a constant value in order to reducethe correlation between the energy loss and the P ID. The obtained χ2 distribution as
The range R can be described as R ∝ T α /(mZ 2 ), where T , m and Z are the kinetic energy, massand charge number of the incident particle, respectively. Now, we defined the path length as b in theprevious layer of the stopping one and x in the stopping layer. In this definition, the path length b + x
and x can be described as b + x ∝ (dEistop + dEistop −1 )α /(mZ 2 ) and x ∝ dEiαstop /(mZ 2 ). Thus, the P ID
parameter should depend on the thickness of the previous layer of the stopping one and the mass andαfiff i )α ) · cos θ ∝ mZ 2 (b cos θ).
charge of the incident particle as P ID = ((dE− (dEstop + dE (istop −1) )stop
14.3. GAIN CALIBRATION

107

a function of α is shown in Figure 4.10. The optimum α parameter was determined byfitting it with a second order polynomial function.
(a): α = 1.58(b): α = 1.73
50〜
dE in the 2nd layer [MeV]〜dE in the 2nd layer [MeV]

50
40

p

30
20
10
0
0

100

200

300

400

500

40

p

30
20
10
0
0

600
PID

100

200

300

400

500

600
PID

Figure 4.9: A typical scatter plot between the energy deposit of the second layer and
P ID for the istop = 2 event. In this figure, the parameter α was set at 1.58 and 1.73
in (a) and (b), respectively. The stopping proton cluster were fitted with the constantvalue shown as red lines.
550

500

χ2

450

400

350

300
1.58

1.6

1.62

1.64

1.66

1.68

1.7

1.72

α

1.74

Figure 4.10: A typical χ2 distribution as a function of α when we fit the scatter plot
between the energy loss at stopping layer and PID with constant value as Figure 4.9.
The optimum α parameter was determined by fitting with the second order polynomial
function shown as a black line.

108

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS

4.4

Particle identification in RCA

Proton was selected by combining the information of the stopping layer (istop ), velocity and the P ID parameter. In this section, we describe the proton selection scheme
for each stopping layer. The scheme to evaluate the π ± contamination yield for eachstopping layer is also described in this section. In the proton-selection region, there
are also some contamination from π ± because the charged pions are influenced not only
from electromagnetic processes but also strong interaction processes such as π − nuclear
absorption.

Analysis for stopping layer istop = 2 ∼ 4

4.4.1

In the cases of the stopping layers from istop = 2 to istop = 4, proton events were selectedwith the information of 1/β and P ID. Figure 4.11 shows scatter plots between 1/β and
P ID for each istop case. In these figures, we can see three clusters. A cluster in 1/β ∼ 1
was corresponding to leakage particles at the side edge of RCA and the others wereoriginated from the charged pions and protons stopping at each layer. In this analysis,
proton was selected as the gate of ± 3σ in P ID and ± 2σ in 1/β shown in the red boxes.
These σ’s were obtained by fitting the proton distributions with Gaussian functions inthe (π + , π + ) and (π + , p) reaction events obtained with the TOF-RCA trigger.

(a): i stop = 2(c): i stop = 4

4

4

3.5

3.5

3.5

3

3

π

2.5

1/β

2.5

p

2

p

π

2.5

1/β

3

1/β

(b): i stop = 3

4

2

2

1.5

1.5

1.5

1

1

1

0.5

0.5

0.5

0
0

100 200 300 400

500 600

PID

0
0

200

400

600

800

PID

0
0

π

200

p

400

600

800

PID

Figure 4.11: A typical scatter plots between the 1/β and P ID for the istop = 2, 3 and4 events shown in (a), (b) and (c), respectively. The proton selection gates are shownwith the red boxes.

4.4. PARTICLE IDENTIFICATION IN RCA

109

Figure 4.12 shows the P ID spectra for each stopping layer; the black and gray histograms corresponding to the spectra with and without proton selection in 1/β, respectively. The proton-selection region (± 3σ) is also shown with red lines. The contamination yield of the π ± in the proton selection region was investigated with the events inthe π ± contamination gates shown with black lines. The π ± contamination gates wereset from both higher and lower side region to keep the same gate width with the proton
selection gate.
(a): i stop = 2
1000(c): i stop = 4(b): i stop = 3

w/o 1/β cut

220

w/o 1/β cut

w 1/β cut200

w 1/β cut

w/o 1/β cut
w 1/β cut

500

180

800

160

400

120
100

400
Proton selection200

π± contamination gate80

π± contamination gate

Counts

600

CountsCountsProton selection140

π± contamination gate

π± contamination gate

300
Proton selection

200

60

π± contamination gate40

π± contamination gate

100

20
0
0

100 200 300 400

500 600

PID

0
0

200

400

600

800

PID

0
0

200

400

600

800

PID

Figure 4.12: A typical P ID spectra for the istop = 2, 3 and 4 events shown in (a), (b)and (c), respectively. The black and gray spectra are indicated with and without proton
selection of the 1/β, respectively. The proton selection gates and π ± contamination gatesare also shown in these figures.

4.4.2

Analysis for stopping layer istop = 1

In the case of stopping layer istop = 1, we can not define the P ID because of a lack ofenergy deposit information in the second layer. Therefore, we selected proton by using
the energy deposit in the first layer, which was same as the total energy, and the velocity(1/β) only.
Figure 4.13 (a) shows a typical scatter plot between the 1/β and energy deposit in
the first layer of RCA. In the figure, we can see a clear locus of a proton cluster stoppingfin the first layer. The correlation (dE–1/β)
was fitted with a second order polynomial
in 1/β (f (1/β)) shown as a red line. We selected the proton stopping at the 1st layer inf - f (1/β) as shown in Figure 4.13 (b). Here, the small energy-loss events
the gate of dE
f < 2 MeV) was rejected in order to reduce background.
(dE

110

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSISIn Figure 4.13, we can see another proton cluster which did not stop inside the RCA
and leaked at the side edges of scintillator indicated with a green arrow. Therefore, we
set the π ± contamination gate only for higher 1/β side region for the stopping layer
istop = 1 assuming the flat distribution shown as Figure 4.13 (b) in order to avoid theseleakage protons.
(a)

(b)

600

45

Proton selection

40

〜

400

30
25

CountsdE in the 1st layer [MeV]

500
35

p

20

300

200

15
10

π± contamitation gate

100
5
0

1

2

3

4

5

6

7

1/β

0
-10 -50

5

10 15 20 25 30

dE - f(1/ β)

Figure 4.13: (a) A typical scatter plot between the 1/β and energy deposit of the firstlayer of RCA. (b) The proton selection gate and the side band region as the function off - f (1/β). See the text for the detail.
dE

4.4. PARTICLE IDENTIFICATION IN RCA

4.4.3

111

Analysis for stopping layer istop = 5

In the analysis of istop = 5, we can not obtain the range information from the hit patternin RCA because these events had the hits for all the layers of RCA. Thus, we identified
the proton by using the information of β, P ID and energy deposit of the fifth layerof RCA. As shown in Figure 2.20 (b), the expected maximum proton momentum fromthe K − pp signal is almost 800 MeV/c, whose velocity is βpmax = 0.65. We show theeﬀective range, which is considered maximum incident angle to RCA, as a function of
β for the pion and proton in Figure 4.14. In order to reach the fifth layer, the pion’s
velocity should be more than βπ > 0.7. Therefore, we could select the proton less than
800 MeV/c by choosing the event of β < 0.65 = βpmax for istop = 5 in principle.
Momp = 800 MeV/c

Effective range [cm]Layer5pπLayer4Layer3Layer2
Layer1βFigure 4.14: The eﬀective range for the pion (black points) and proton (red points) as afunction of β. In this figure, the depth for perpendicularly and maximum incident angle
case are shown. The thickness of each layer of RCA is also indicated in the figure.
Figures 4.15 (a) and (b) show typical scatter plots between P ID and energy depositin the fifth layer of RCA without and with the β < 0.65 cut, respectively. In thisfigure, we can see three clusters. One is a cluster of pions, which penetrate all the layers,
indicated by a blue arrow in Figure 4.15 (a). Next, we can see a cluster of protons, which
penetrate all the layers, indicated by a red arrow in Figure 4.15 (b). The last cluster iscorresponding to the proton stopping in the fifth layer indicated by a magenta arrow in
Figure 4.15 (b).
Most of the pions could be suppressed by applying the β < 0.65 cut as shown in Figure 4.15 (a) and (b). However, some pions still remained as observed in Figure 4.15 (b)(blue ellipse region). These pions might be understood caused not only from the electromagnetic processes but also from strong interaction processes. Moreover, the muonfrom the π ± decay in flight can also remain in the β < 0.65 cut. We chose the proton
selected as the red points shown in Figure 4.15 (c) to avoid the penetrate pions. The π ±contamination was estimated from the events in the side region of this selected region in
the scatter plot.

112

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS(a): w/o β cut〜

dE in the 5th layer [MeV]

100
90
80
70
60
50

π

40
30
20
10
100

200

300

400

500

600

PID
(b): w β < 0.65 cut〜

dE in the 5th layer [MeV]

100
90
80

p

70
60
50

p

π

40
30
20
10
100

200

300

400

500

600

PID
(c): w β < 0.65 cut〜

dE in the 5th layer [MeV]

100
90
80

All eventProton selected event

70
60
50
40
30
20
10
100

200

300

400

500

600

PID

Figure 4.15: A typical scatter plot between P ID and energy deposit of the fifth layer of
RCA for the istop = 5 event. The scatter plot without and with β < 0.65 cut are shownin (a) and (b), respectively. The events selected as the proton is shown with the redpoints in (c).

4.5. DETECTION EFFICIENCY OF RCA

4.5

113

Detection eﬃciency of RCA

The overall eﬃciency of the RCA for protons and pions was evaluated by using thep(π + , K + )Σ+ reaction at pπ+ = 1.69 GeV/c. In this reaction, at first we can identify
the Σ+ production in the (π + , K + ) missing-mass. Further, we can measure the protonand π + from the Σ+ decay (Σ+ → pπ 0 or Σ+ → nπ + ) with RCA in coincidence. Since
the velocities of the proton and π + from the Σ+ decay are diﬀerent, we can distinguishbetween proton and π + by using only the information of 1/β in this reaction.

Momentum (proton) [MeV/c](a): π+ p → K+ Σ+, Σ+ → p π0
800
700

Seg6

Seg5

Seg4

Seg1

Seg2

Seg3

350
300

600
500

250

400

200

300

150

200

100

100

50

0

-100

-50

0

50

100

0

θxz(Lab) (proton) [degree](b): π+ p → K+ Σ+, Σ+ → n π+

Momentum (π+) [MeV/ c]

400
350

Seg6

Seg5

Seg4

Seg1

Seg2

Seg3

250

300
200

250
150

200
150

100

100
50

50
0

-100

-50

0

50

100

0

θxz(Lab) (π ) [degree]+

Figure 4.16: The simulated correlation plot between produced angle of the xz plane(θxz ) and the momentum of proton and π + from the Σ+ decay are shown in (a) and (b),respectively. The acceptance of each segment of RCA is also indicated as the red box.
Figure 4.16 shows the correlation between produced angle in the xz plane (θxz ) andmomentum of proton (a) and π + (b) estimated from a simulation taking account ofelementary diﬀerential cross section. The acceptance of each segment is also indicatedas a red box. In this plot, the emitted K + was required to be detected with the SKS andthe asymmetry of the left and right originated from the asymmetry of the acceptance of
the SKS for the K + .

114

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS(a): Seg1

120(b): Seg4

data

π

160

160

data

140

simulation

simulation (π )140simulation (p)

100

data

π

simulation (π )(c): Seg4 w proton selction

simulation (p)

120

120

100

100

60

CountsCountsCounts

80

80

60

80

60

40

p

40
20

p

40

20

0

20

0
1

2

3

4

5

6

7

1/β

0
1

2

3

4

5

6

7

1/β

1

2

3

4

5

6

7

1/β

Figure 4.17: (a, b) The obtained 1/β spectrum for the Seg1 and 4 of RCA in coincidencewith Σ+ production shown. The simulated 1/β distributions of the proton and the otherparticles (dominant component was π + ) from the Σ+ decay are also shown in red and bluelines, respectively. (c) The proton selection events in the scheme described in Sec. 4.4
for data and simulation shown in black points with error bar and red line, respectively.

As shown in Figure 4.16 (a), the proton from the Σ+ decay can reach the Seg1 and4, which are the most forward segments of RCA, while π + can reach all the segments.
Figures 4.17 (a) and (b) show the obtained 1/β spectra of the Seg1 and 4, respectively,in black lines. In this spectrum, the Σ+ produced events were selected by checking themissing mass of p(π + , K + ) reaction. The simulated 1/β distributions of the proton andother particles, from the Σ+ decay are also shown in red and blue lines, respectively. Since
the dominant component of other particles was π + , we describe such a component as theπ + simply although gamma and electron were also contaminated with small fractions.
In order to compare the data with simulation, we applied a cut for the energy loss in thef > 1.3 MeV, both in the simulation and data analysis. The π +first layer of RCA, dE
and proton are separated in the 1/β shown as the arrow in these figures.
The yield of the simulation was normalized by adjusting the detected K + yield assame as the observed one. We found that the yield of π + and proton were almost consistent between data and simulation as shown in Figure 4.17 (a) and (b). A coincidence
probability of π + (ηπ ) defined as,∫
1
N (π in RCA)
dσπ
=
dΩ,
(4.3)
ηπ =
ϵπ
+
N (Σ detected)
4π ΩRCA dΩπwhere ΩRCA is geometrical acceptance of RCA, dσ
is diﬀerential cross section of π + ofdΩ++the Σ → nπ decay including the branching ratio (48.3%). ϵπ is eﬃciency to identify
the π (assuming ∼100 % because we only use the information of the first layer), of eachCoincidence probability

4.5. DETECTION EFFICIENCY OF RCA

115

data

0.04

simulation

0.035
0.03
0.025
0.02
0.015
0.01

1

2

3

4

5

6

Segment of RCA
Figure 4.18: The π + coincidence probability, which is defined as Eq. 4.3, of each segmentof RCA. The present data and simulated one are shown by crosses and open circles,
respectively.

segment of RCA for data and simulation is summarized in Figure 4.18. These values
for data and simulation are almost consistent with each other. Thus, we understand thegeometical acceptance of RCA reasonably well.
Next, we discuss the proton coincidence probability by using the Seg4 because theyield of proton in Seg1 is limited. In the p(π + , K + ) reaction, we can separate π + andproton by using only the 1/β information shown as the arrow in Figure 4.17 (b). Thus,
we defined the coincidence probability of proton for the first layer (ηp(1st) ) as,N (p in RCA)1
ηp(1st) ==+N (Σ detected)
4π∫ϵp(1st)
ΩRCA

dσp
dΩ,
dΩ

(4.4)

where N (p in RCA) is the number of proton events to be detected in the first layerof RCA shown in Figure 4.17 (b) and ϵp(1st) is the eﬃciency to identify the proton inp
is diﬀerential cross section of
the first layer assumed to be ∼100 % in this analysis. dσdΩ+0
proton from the Σ → pπ decay including the branching ratio (51.6%). The coincidence
probabilities for the first layer obtained from the data and simulation are 2.8 ± 0.1%
and 3.4%, respectively.
Fig. 4.17 (c) shows the proton events in the scheme as described in Sec. 4.4 for thedata and simulation in black points with error bars and a red line, respectively. The
overall proton coincidence probability (ηp ) is defined as,
1
N (p selected in RCA)=ηp =+N (Σ detected)
4π

∫
ϵp
ΩRCA

dσp
dΩ,
dΩ

(4.5)

116

CHAPTER 4. ANALYSIS II - COINCIDENCE ANALYSIS

where N (p selected in RCA) is the number of proton events selected with the scheme
described in Sec. 4.4 shown in Figure 4.17 (c) and ϵp is the detection eﬃciency for the
proton in RCA. In this Σ+ analysis, we could estimate the proton detection eﬃciency ϵpas,
N (p selected in RCA)
,
(4.6)
ϵp =
N (p in RCA)
where N (p in RCA) is the number of proton events identified with only the first layer of
RCA same as Eq. 4.4. The overall proton coincidence probabilities (ηp ) of Seg4 for thedata and simulation are 1.8 ± 0.1% and 2.7%, respectively. The detection eﬃciency (ϵp )for the data and simulation are 65% and 78%, respectively. The main component of anineﬃciency of ϵp originates from the leakage of proton at the side edge of RCA and it
strongly depends on the incident angle to the RCA. As shown in Figure 4.16 (a), theprotons produced from the Σ+ decay concentrate in the forward angle and we can detect
only a tail part of this Σ+ decay. Thus, the discrepancy of the proton detection eﬃciency
between the data and simulation by 20% may originate from not an ambiguity of the
proton detection eﬃciency itself but the reproducibility of the proton incident angle
distribution. From this study, we found that the absolute detection eﬃciency might beoverestimated by 20%. We discuss the uncertainty of the cross section caused from thisambiguity in Sec. 5.2.6.

Chapter 5
Experimental results and discussion
The experimental results are separated into two parts; namely the inclusive analysis
results and the coincidence analysis results. At first, we discuss the inclusive spectra of
the d(π + , K + )X reaction by comparing the Monte Carlo simulations based on a simple
quasi-free picture. In the next section, the coincidence analysis results with RCA are
discussed.

5.1

Inclusive analysis: results and discussion

5.1.1

Inclusive missing-mass spectra of the d(π + , K + ) reaction

As mentioned in Sec. 3.1, we can define M Md and M Mp as follows√
M Md(p) = (Eπ + Md(p) − EK )2 − (p2π + p2K − 2pπ pK cos θπK ),(5.1)

where M Md and M Mp are the missing mass calculated assuming the deuteron and proton
at rest as a target, respectively. Here, Md and Mp are the rest mass of deuteron andproton, respectively.
Figures 5.1 (a) and 5.2 (a) show missing-mass spectra in the scattering angle of 2◦
to 16◦ in the laboratory system, before corrections with experimental eﬃciency and theacceptance of the SKS, in the d(π + , K + ) reaction expressed as the M Md and M Mp ,respectively. Figures 5.1 (b) and 5.2 (b) show the double diﬀerential cross sections after
the corrections with experimental eﬃciency and acceptance of the SKS as described in
Eq. 3.30. The spectra are shown with a bin width of 2 MeV/c2 per bin.
In these spectra, we can find three major peak structures around 2.08 (1.12) MeV/c2 ,2.17 (1.19) MeV/c2 and 2.40 (1.37) MeV/c2 in the M Md (M Mp ) spectrum. These
regions are shown as I, II and III in Figures 5.1 and 5.2. These peaks can be considered
as originating from the Λ, Σ and hyperon resonance (Y ∗ ) productions in the quasi-freeprocesses.

117

118

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSIONCounts / (2MeV/c2)

14

I

(a)
II

d σ /d Ω/dM 2o-16o(Lab) [µb/sr/(MeV/c2)]

×103

(b)

14

III

12

12

10

10

8
6
4

6
4
2

2

2

8

0

2.1

2.2

2.3

2.4

0

2

2.1

2.2

2.3

2.4

MM d [GeV/c2]

MM d [GeV/c ]Figure 5.1: The obtained inclusive missing-mass spectra of the d(π + , K + ) reaction at
1.69 GeV/c as a function of missing mass M Md . The spectra of raw missing-mass anddouble diﬀerential cross section are shown in (a) and (b), respectively.

I

(a)
II

d σ /d Ω/dM 2o-16o(Lab) [µb/sr/(MeV/c2)]

18

×103

18

III

16

Counts / (2MeV/c2)

(b)

16

14

14

12

12

10

10

8
6
4

6
4
2

2

2

8

0

1.1 1.15 1.2 1.25 1.3 1.35 1.4
2

MM p [GeV/c ]0

1.1 1.15 1.2 1.25 1.3 1.35 1.4

MM p [GeV/c2]

Figure 5.2: The obtained inclusive missing-mass spectra of the d(π + , K + ) reaction at
1.69 GeV/c as a function of missing mass M Mp . The spectra of raw missing-mass anddouble diﬀerential cross section are shown in (a) and (b), respectively.

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

5.1.2

119

Quasi-free processes in the d(π + , K + ) reactions

In the d(π + , K + ) reaction at pπ = 1.69 GeV/c, there are several quasi-free processes
known from old elementary process data. Here, we considered the quasi-free hyperon
productions of Λ (Region I) and Σ+/0 (Region II),
π + “n” → K + Λ,
π + “p” → K + Σ+ ;(5.2)

π + “n” → K + Σ0 ,(5.3)

hyperon resonance (Y ∗ ) productions of Λ(1405) and Σ(1385)+/0 (Region III),
π + “n” → K + Λ(1405),
π + “p” → K + Σ(1385)+ ;(5.4)

π + “n” → K + Σ(1385)0 ,(5.5)

and non-resonant productions of Λπ and Σπ (Region III),
π + “N ” → K + Λπ;

π + “N ” → K + Σπ.

(5.6)

The “n” and “p” indicate a neutron and a proton in a deuteron, respectively. The crosssections of elementary processes have already been measured [65, 19] and these total
cross sections σ are listed in Table.5.1.

0.016
0.014

a.u.

0.012
0.01
0.008
0.006
0.004
0.002
0
0

50

100

150

200

250

300

Momentum [MeV/ c]

Figure 5.3: The momentum distribution of a nucleon inside of deuteron obtained fromthe Bonn Potential [97].

We made an attempt to reproduce the double diﬀerential cross section d2 σ̄/dΩ/dMwith a Monte Carlo simulation by using the diﬀerential cross sections dσ/dΩ of eachelementary reaction obtained in the past experiments with a smearing by the nucleon
Fermi motion in a deuteron. We assumed there are no rescattering of all the final stateparticles such as K + , hyperon, Y ∗ ’s etc. Here, we used a deuteron wave-function derived
from the Bonn potential [97], of which nucleon momentum distribution (pF ) is shown

120

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

in Figure 5.3. In this simulation, the participant nucleon mass, Mp∗ , was assumed to bein the oﬀ-mass by taking into account the Fermi motion, pF , as:
(
)2
√
∗2
2
2
Mp = Md − Ms + pF − p2F ,(5.7)
where Md and Ms are deuteron and spectator on-shell nucleon mass, respectively (spectator model [100]). The emitted K + momentum, pK , was distributed according to thereaction kinematics with the mass of the the participant nucleon Mp∗ and its momentump⃗F . Then, the missing mass M Md was calculated as M Md2 = (Eπ +Md −EK )2 −|p⃗π −p⃗K |2 .
Table 5.1: Elementary total cross sections of hyperon productions. The cross sections of
π + p reaction at 1.7 GeV/c are listed in the left [65]. The cross sections of π + n reaction
at 1.69 GeV/c, which is assumed the isospin symmetry, are listed in the right [19].
Reaction(π + p)

Cross section (µb)π + p → K + Σ+

470 ± 39

π + p → K + Σ(1385)+
π + p → K + Λπ
π + p → K + Σπ

124 ± 2040.0 ± 28
40.0 ± 6.0

Reaction(π + n)π+n → K +Λπ + n → K + Σ0
π + n → K + Λ(1405)
π + n → K + Σ(1385)0
π + n → K + Λπ
π + n → K + Σπ

Cross section (µb)
174 ± 14121 ± 10
20.6 ± 1.0
76.7 ± 1013.7 ± 1.8
19.3 ± 1.0

180
160
140
120

π+p→K+Σ+

100
80
60
40
20
0
-1 -0.8 -0.6 -0.4 -0.2 070dσ/dΩCM [ µb/sr]

dσ/dΩCM [ µb/sr]

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

0.2 0.4 0.6 0.8

50
40
30
20

0
-1 -0.8 -0.6 -0.4 -0.2 01cosθ(CM)12dσ/dΩCM [ µb/sr]

dσ/dΩCM [ µb/sr]

π+n→K+Σ010

π p→K Σ(1385)+

18
+
+
16
14
12
10
8
6
4
2
0
-1 -0.8 -0.6 -0.4 -0.2 0

60

10

0.2 0.4 0.6 0.8

8
6
4

0
-1 -0.8 -0.6 -0.4 -0.2 0

1

6

+

40
30
20
10

0.2 0.4 0.6 0.8

1cosθ(CM)

π n→K Λ0
-1 -0.8 -0.6 -0.4 -0.2 01cosθ(CM)2dσ/dΩCM [ µb/sr]

dσ/dΩCM [ µb/sr]

50+

0.2 0.4 0.6 0.8

π+n→K+Σ(1385)0cosθ(CM)
60

121

5

π+n→K+Λ(1405)

4
3
2
1

0.2 0.4 0.6 0.8

1cosθ(CM)0-1 -0.8 -0.6 -0.4 -0.2 0

0.2 0.4 0.6 0.8

1cosθ(CM)

Figure 5.4: Considered elementary diﬀerential cross sections of the two-body reactions
for the quasi-free processes obtained from the Ref. [65, 19]. These values are plotted in
the center of mass system.

122

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

For the π + + “n” reactions, we used the cross sections and angular distributions of
π + p reactions in Ref. [19] assuming isospin symmetry. For the π + + “p” reactions,
we used the values in Ref. [65]. The∑ angular distributions were expressed as Legendre
polynomial functions as, dσ/dΩ =An Pn (cos θ), in the past experiments. Here, in thecases of π + p → K + Σ+ and π + p → K + Σ(1385)+ reactions, fit results with a Legendre
polynomial function were not given in Ref. [65]. Therefore, we estimated these parameters by ourselves by fitting the listed data in Ref. [65]. The fit reproduces the measured
diﬀerential cross sections of the p(π + , K + ) reaction at 1.69 GeV/c reasonably well.
All considered elementary diﬀerential cross sections of the two-body reactions are
summarized in Figure 5.4. Three-body reactions such as π + n → K + Λπ reaction wereassumed to be distributed in a three-body phase space. Moreover, the elementary diﬀerential cross section for the Σ0 production processes [19, 98, 99] features rather large errors
in the forward scattering angles as shown in Figure 5.5. Therefore, an adjustment of thenormalization of the cross section of the quasi-free Σ component was applied within themeasurement errors in the present simulation.
−450
Thomas et al.

400dσ/dΩLab [µb/sr]

Hart et al.

350

Dahl et al.

300
250
200
150
100
50
0
0

2

4

6

8

10

12

14

16

θ(Lab) [deg]Figure 5.5: The diﬀerential cross sections of the Σ0 production in the p(π − , K 0 )Σ0 reaction for the forward scattering angle obtained from the Ref. [19, 98, 99].

A simulated spectrum as a sum of each quasi-free process is shown in Figure 5.6. An
enlarged spectra in Region III is also shown in Figure 5.7.

d σ /d Ω/dM 2o-16o(Lab) [µb/sr/(MeV/c2)]

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

123

Total
π+"n" → K+Λ
π+"p" → K+Σ++
π+"n" → K Σ0+
π "n" → K+Λ(1405)
π+"n" → K+Σ(1385)0++π+"p" → K Σ(1385)
π+"p" → K+Λπ
π+"n" → K+Λπ
π+"p" → K+Σπ
π+"n" → K+Σπ

6
5
4
3
2

2

1
0

2.1

2.2

2.3

2.4
2.5
MM d [GeV/c2]

1.4

Total

1.2

π+"n" → K+Λ
π+"p" → K+Σ+
π+"n" → K Σ0π+"n" → K+Λ(1405)
+

1

0.6

π+"n" → K Σ(1385)0++π+"p" → K Σ(1385)
π+"p" → K+Λπ

0.4

π+"n" → K+Λπ
π+"p" → K+Σπ+

0.8

π+"n" → K+Σπ

0.2

2d σ /d Ω/dM 2o-16o(Lab) [µb/sr/(MeV/c2)]

Figure 5.6: A simulated diﬀerential cross section of the d(π + , K + ) reaction for the quasifree processes. Each process is shown in the figure with diﬀerent colors and line styles.

0

2.3

2.35

2.4

2.45
2.5
MM d [GeV/c2]

Figure 5.7: An enlarged spectrum of Figure 5.6 in Region III.

124

Discussion on inclusive spectra2d σ /d Ω/dM 2o-16o(Lab) [µb/sr/(MeV/c2)]

5.1.3

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

Σ

6

data

5
4

simulation

Λ

3
2

Y*

1
0

2.1

2.2

2.3

2.4
2.5
MM d [GeV/c2]

Figure 5.8: The missing-mass spectrum (M Md ) of the d(π + , K + ) reaction for the scattering angle from 2◦ to 16◦ in the laboratory system per 2 MeV/c2 . The crosses and solidline show the experimental data and the simulated spectrum, respectively. The resultof the Y ∗ peak fitting is also shown with a dashed red line for the experimental data.
Taken from Ref. [93].

Figure 5.8 shows the obtained double diﬀerential cross section (crosses) comparedwith the simulated spectrum (solid line). We find an overall structure of the spectrum
is well reproduced expect for two distinct diﬀerences. One diﬀerence is a cusp structure
observed around 2.13 GeV/c2 . The other diﬀerence is a “shift” of the broad bumpposition for the Y ∗ production in Region III.

ΣN cusp
A magnified view of the missing-mass spectrum in Region I is shown in Figure 5.9 (a)for the forward scattering angle from 2◦ to 8◦ in the laboratory frame. A peak aroundΣN thresholds (2.1289 GeV/c2 for Σ+ n and 2.1309 GeV/c2 for Σ0 p) is prominent in the
figure. When we chose the scattering angle larger than 8◦ , the cusp is less prominent
due to the large quasi-free Λ and Σ backgrounds as shown in Figure 5.9 (b).
Generally, when a new threshold opens, a cusp structure can appear in order toconserve the flux and the associated unitarity of the S-matrix. However, such a cusp
structure can not always be observed at the threshold experimentally. On the other hand,similar cusp structure can also be seen when a pole exists near the threshold [101]. In caseof the ΣN system, it is theoretically suggested that the pole exists near the ΣN thresholdin a second and third quadrant of the complex plane of the ΣN relative momentum using

12d σ /d Ω/dM 8o-14o(Lab) [µb/sr/(MeV/c2)]

14

Σ

(a)

10
8
6

Λ

4
2

3.5
3
2.5

125

Σ

(b)

Λ

2
1.5
1
0.5

2

2

d σ /d Ω/dM 2o-8o(Lab) [µb/sr/(MeV/c2)]

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

0

2.1

2.12

2.14

2.16

MM d

[GeV/c2]

0
2.05

2.1

2.15

2.2

MM d [GeV/c2]

Figure 5.9: (a)The missing-mass spectrum (MMd ) in 2.09 to 2.17 GeV/c2 region for theforward scattering angle from 2◦ to 8◦ (Lab) per 0.5 MeV/c2 , which is shown by crosses.
The fitting results are shown by solid and dashed lines (χ2 /ndf = 1.11). Taken from
Ref. [93]. See the text for the detail. (b)The missing-mass spectrum (MMd ) in 2.05 to
2.20 GeV/c2 region for the backward scattering angle from 8◦ to 14◦ (Lab) per 0.5 MeV/c2
shown by crosses. The cusp is less prominent due to the large quasi-free backgrounds
when we select the backward scattering angle.

126

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

the several Y N potential models by Miyagawa and Yamamura [102]. Thus, the structure
at the ΣN threshold would not be a simple threshold eﬀect but could originate from apole near the ΣN threshold. Experimentally, a cusp structure at the ΣN threshold
was observed in K − d → π − Λp reaction more than 40 years ago [103, 104]. Figure 5.10
shows the obtained Λp invariant-mass spectrum in the K − d → π − Λp reaction at rest
in Ref. [103]. A clear peak corresponding to the ΣN cusp is seen around 2.13 GeV/c2 .
Recently, the ΣN cusp has been intensively investigated in the pp → K + Λp reaction at
COSY [105, 106]. These results were listed in Ref. [107].

Figure 5.10: The obtained Λp invariant mass spectrum of the old experiment in theK − d → π − Λp reaction at rest taken from Ref. [103]. The clear structure corresponding
to the ΣN cusp is seen around 2.13 GeV/c2 .

Although this ΣN cusp may not necessarily distribute according to a Lorentzianfunction, here we fit the cusp structure with this function in order to compare with theprevious results summarized in Ref. [107]. Through a fit of the Lorentzian function foldedwith the resolution of 1.4 MeV/c2 . in σ for the cusp (solid line) and a third-order polynomial function for a continuum background (dashed line), we obtained the peak position at+0.6
2130.5 ± 0.4 (stat.) ± 0.9 (syst.) MeV/c2 , the width of Γ = 5.3 +1.4
−1.2 (stat.) −0.3 (syst.) MeV
and the diﬀerential cross section of dσ̄/dΩ = 10.7 ± 1.7 µb/sr.
The statistical errors were estimated from the χ2 distribution of the fitting as a function of the peak position and width of the cusp shown in Figure 5.11. In this fit, there
were seven parameters, which correspond to the peak position, the width and the normalization factor for the Lorentzian function (ΣN cusp) and four parameters for the thirdorder polynomials (continuum background). Thus, the χ2 value was calculated by adjusting the parameters except for the peak position and the width to vary for minimizing χ2
for each combination of the peak position and the width. The systematic errors of thesevalues were estimated in σ taking into account uncertainties in the absolute momentum
scale of ± 1.1 MeV/c fitting ranges, the missing-mass resolution (± 0.08 MeV/c2 ), thebinning of the missing-mass spectrum and background functional shapes by changing

115

8

decay width (Γ) [MeV]

127

χ2

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

110

7

105

6

100
95

5

90

4

2129.5852130

2130.52131

2131.580

peak position [MeV]

Figure 5.11: The contour plot of the χ2 of the fitting shown in Figure 5.9 (a) as a functionof the peak position and width. The black lines show ∆χ2 = +1, +2 and +3 regions fromthe minimum χ2 value shown in a cross. The red lines show the 1σ and 2σ deviations.

the third to fifth order polynomials. The χ2 /ndf of this fitting was 1.11. This result isthe first observation of the ΣN cusp structure in the inclusive spectrum of the d(π + , K + )reaction.
In Ref. [107], the obtained spectrum from these past experiments were fitted witha Lorentzian function after subtracting the continuum background. The obtained peak
position and width from this fitting are shown in Figure 5.12 [107]. Furthermore, since
existence of a shoulder at about 10 MeV higher mass was reported in several reactions,they also tried to fit with two Lorentzian functions. The obtained peak positions andwidths corresponding to two Lorentzian functions are listed in Figure 5.13 [107].
The obtained peak position from the present analysis is consistent with the meanvalue shown in Figure 5.12, which is the one Lorentzian fitting result, within the errors.
The same was true with the lower peak (m01 ) shown in Figure 5.13 for two Lorentzian
fitting results. Here, we can conclude nothing on the existence of the shoulder structure(higher peak m02 ) from the present data because of the large quasi-free Σ backgrounds.
In addition, the width seems to be smaller than the averaged value of 12.2 ± 1.3 MeV
in other reactions shown in Figure 5.12, although there is no large diﬀerence between thewidth of lower peak (Γ1 ) in Figure 5.13. In order to discuss the possible pole position andthe diﬀerence between the other reaction data, we need realistic theoretical calculations
taking into account the (π + , K + ) reaction mechanism. Such a detailed studies including
the present data would reveal the information of the ΣN –ΛN coupling strength.

128

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

Figure 5.12: A summary of the peak positions (m0 ) and widths (Γ) from the fit with one
Lorentzian function by the author of Ref. [107]. The values for the data set from Braun etal. [104], Eastwood et al. [108], Pigot et al. [109], Tan [103], SPES4 [110], HIRES [105]and TOF [106] are shown. The lines show the mean (thick line) and variance (thin line).
The arrows show the indicated thresholds.

Figure 5.13: A summary of the peak positions (m01 , m02 ) and widths (Γ1 , Γ2 ) from thefit with two Lorentzian functions by the author of Ref. [107]. The used data sets aresame as in Figure 5.12. The lines show the mean (thick line) and variance (thin line).
The arrows show the indicated thresholds.

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

129“Shift” of Y ∗ peak
In Region III, the contributions of Σ(1385)+/0 and Λ(1405) overlap each other, and it is
not possible to disentangle them in the inclusive measurement. Here, we treat the bump
structure as one component.
When we fitted the bump with a Gaussian function, we obtained the peak position at 2400.6 ± 0.5 (stat.) ± 0.6 (syst.) MeV/c2 for the present data and at22433.0 +2.8
−1.6 (syst.) MeV/c for the simulation as shown in Figure 5.8. The systematic error for the simulation was estimated taking into account uncertainties of the diﬀerential
cross sections of Y ∗ , the Y ∗ mass and fitting ranges. The same fitting procedure wasapplied for a M Mp spectrum. We obtained the peak position at 1376.1 ± 0.4 (stat.)2± 0.5 (syst.) MeV/c2 and 1398.5 +2.6
−1.6 (syst.) MeV/c , respectively. The amount of
the peak shift for the scattering angle of 2◦ to 16◦ is 32.4 ± 0.5 (stat.) +2.9
−1.7 (syst.)
2(22.4 ± 0.4 (stat.) +2.7
(syst.))
MeV/c
for
the
M
M
(M
M
)
spectratothelow mass
d
p
−1.7
side.
Even if the peak position of the simulated spectrum was adopted instead of the fitted
one, the diﬀerence is only reduced by just 4 MeV/c2 . There could be an additional
uncertainty by several MeV additionally to the low-mass side arising from our simple
spectator model in the simulation, which was estimated from the diﬀerence of the peak
positions when the balance of the oﬀ-shellness between the participant and spectator
nucleons was changed. The small diﬀerence of about 3 MeV/c2 for the quasi-free Σ
productions is within this uncertainty. More sophisticated theoretical analyses taking
into account Y ∗ N interactions in the final state might explain the observed puzzling“shift”.
Next, we discuss the comparison of the Y ∗ bump for each scattering angle between
the obtained data and the simulation. Figures 5.14 and 5.15 show the spectra obtained
from data and simulation for the M Md and M Mp , respectively, for every 2◦ between 2◦
and 16◦ . The peak positions of Y ∗ for the present data are shifted to low mass side forall the scattering angles. The same fitting procedure as for the angle averaged spectrain the whole scattering angle was applied for each spectrum.
The obtained peak positions are summarized in Figure 5.16. The peak position of thesimulation for M Mp spectra (black points with error bars in Figure 5.16 (b)) decreaseas the scattering angle becomes larger. It is because the elementary cross section of
Λ(1405) is larger (smaller) than that of Σ(1385) in the very forward (backward) region.
So that the peak position is larger in the forward scattering angle. However, this eﬀect
shifts the peak by at most 10 MeV. Here, the peak position of the present data for M Mp
spectra (red points with error bars in Figure 5.16 (b)) does not decrease as the scattering
angle becomes larger. On the other hand, the peak positions for M Md spectra (black
points with error bars in Figure 5.16 (a)) increase as the scattering angle becomes larger
because the momentum transfer increases when we select the backward scattering angle.
This increase is seen for the peak position of the present data for M Md spectra (redpoints with error bars in Figure 5.16 (a)).
It should be noted that the LEPS group recently reported a similar inclusive spectrum for the d(γ, K + π − ) reaction at a 1.5–2.4 GeV photon energy region and foundno significant shift in the Y ∗ region [51]. Moreover, there is an old experiment using
a deuterium bubble chamber [111]. They measured the invariant mass spectrum of130

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSIONΛπ + in the π + d → K + Λπ + (ns ) reaction at incident beam momenta between 1.1 and
2.4 GeV/c2 . The measured mass and width for the Σ(1385)+ are 1386.6 ± 4.4 MeV/c2
and 49 ± 11 MeV, respectively. Thus, the Σ(1385)+ mass measured by the invariant
mass of Λπ + is not shifted to the low-mass side.

2

d2 σ /dΩ/dM4 o-6o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM2 o-4o [µb/sr/(MeV/ c 2 )]5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

θLab = 2o - 4o

1.5
1
0.5
0

2.3

2.35

2.4

2.45

2

131

θLab = 4o - 6o

1.5
1
0.5
0

2.3

2.35

2.4

2

θLab = 6o - 8o

1.5
1
0.5
0

2.3

2.35

2.4

2.45

2

θLab = 8o - 10o

1.5
1
0.5
0

2.3

2.35

2.4

θLab = 10o - 12o

1.5
1
0.5
0

2.3

2.35

2.4

2.45

2

θLab = 12o - 14o

1.5
1
0.5
0

2.3

2.35

2.4

2

d2 σ /dΩ/dM2 o-16 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM14o-16 o [µb/sr/(MeV/ c 2 )]θLab = 14o - 16o

1.5
1
0.5
0

2.3

2.35

2.4

2.45
2

MM d [GeV/c ]2.45

MM d [GeV/c 2 ]MM d [GeV/c ]2

2.45

MM d [GeV/c 2 ]d2 σ /dΩ/dM12o-14 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM10o-12 o [µb/sr/(MeV/ c 2 )]MM d [GeV/c 2 ]22.45

MM d [GeV/c 2 ]d2 σ /dΩ/dM8 o-10 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM6 o-8o [µb/sr/(MeV/ c 2 )]MM d [GeV/c 2 ]2θLab = 2o - 16o

1.5
1
0.5
0

2.3

2.35

2.4

2.45

MM d [GeV/c 2 ]Figure 5.14: The obtained double diﬀerential cross section (crosses) of the π + d → K + X
reaction shown with M Md for each scattering angle compared with the simulated spectra (solid lines).

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

2.5

d2 σ /dΩ/dM4 o-6o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM2 o-4o [µb/sr/(MeV/ c 2 )]132

θLab = 2o - 4o

2
1.5
1
0.5
0

1.3

1.35

1.4

2.5

θLab = 4o - 6o

2
1.5
1
0.5
0

1.3

1.35

2.5

θLab = 6o - 8o

2
1.5
1
0.5
0

1.3

1.35

1.4

2.5

θLab = 8o - 10o

2
1.5
1
0.5
0

1.3

1.35

θLab = 10o - 12o

2
1.5
1
0.5
0

1.3

1.35

1.4

2.5

θLab = 12o - 14o

2
1.5
1
0.5
0

1.3

1.35

2

d2 σ /dΩ/dM2 o-16 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM14o-16 o [µb/sr/(MeV/ c 2 )]θLab = 14o - 16o

2
1.5
1
0.5
0

1.3

1.35

1.4
2

MM p [GeV/c ]1.4

MM p [GeV/c 2 ]MM p [GeV/c ]
2.5

1.4

MM p [GeV/c 2 ]d2 σ /dΩ/dM12o-14 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM10o-12 o [µb/sr/(MeV/ c 2 )]MM p [GeV/c 2 ]
2.5

1.4

MM p [GeV/c 2 ]d2 σ /dΩ/dM8 o-10 o [µb/sr/(MeV/ c 2 )]d2 σ /dΩ/dM6 o-8o [µb/sr/(MeV/ c 2 )]MM p [GeV/c 2 ]2.5

θLab = 2o - 16o

2
1.5
1
0.5
0

1.3

1.35

1.4

MM p [GeV/c 2 ]Figure 5.15: The obtained double diﬀerential cross section (crosses) of the π + d → K + X
reaction shown with M Mp for each scattering angle compared with the simulated spectra (solid lines).

2440

(a)

Y* peak position [MeV/c2]

Y* peak position [MeV/c2]

5.1. INCLUSIVE ANALYSIS: RESULTS AND DISCUSSION

2430
2420
2410
2400
2390

1410
1405

133

(b)

1400
1395
1390
1385
1380
1375
1370

2

4

6

8

10

12

14

16

θLab [degree]

2

4

6

8

10

12

14

16

θLab [degree]

Figure 5.16: The peak positions of the Y ∗ bump for each scattering angle obtained fromthe present data (red) and simulated spectra (black) The values obtained for M Md andM Mp are shown with (a) and (b), respectively.

134

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

5.2

Coincidence analysis: results and discussion

5.2.1

π coincidence analysis

According to our Monte Carlo simulation, a proton emitted from hyperon produced
from the quasi-free processes as Eq. 5.2 ∼ 5.6 rarely hits the RCA. However, pions fromthese quasi-free processes can reach all the segments of RCA. This is the same as in thep(π + , K + )Σ+ reaction described in Sec. 4.5 (especially in Figure 4.16).
Thus, we compared the obtained π coincidence spectra of the d(π + , K + ) reaction andthe simulation of the quasi-free hyperon and hyperon resonance production processes,
whose assumptions were same as described in Sec. 5.1.2. Here, we assigned the events,
which had the hit at least in the first layer of RCA and was not assigned as proton, as π.
The other particles such as gammas should be included in our pion selections, although
the main component is pion. Such other particles were also included in the simulationf > 1.3 MeV)
and the same cut condition for the energy loss at the first layer of RCA (dE
was applied both in the simulation and data analysis.

π coincidence probability

0.5

data
0.4

simulation

0.3
0.2
0.1

I
0
2

II
2.1

2.2

III
2.3

2.4

2.5

MM d [GeV/c2 ]Figure 5.17: A comparison of the π coincidence probability spectra between data andsimulation is shown in red and black lines, respectively. The regions of the quasi-free
productions of Λ (I), Σ (II) and Y ∗ ’s (III), which are same as Figure 5.1, are also indicatedin the figure.

Figure 5.17 shows a comparison of the π coincidence probability spectra as a functionof M Md between data and simulation. In the spectra, three regions I, II and III are shownin the figure for diﬀerent quasi-free processes. The diﬀerence originated from the decaybranch to emit the charged pion and the number of the produced charged pions.
For instance, Σ(1385)+ mainly decays to Σ(1385)+ → Λπ + → pπ − π + (55.6%). On
the other hand, Σ+ can decay to nπ + (48.3%). Then, the pion coincidence probabilityof Σ(1385)+ should be higher than the one of Σ+ because Σ(1385)+ and Σ+ can produce

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

135

two and one pion(s), respectively. Such a tendency can be seen in the obtained data
shown in red crosses. Moreover, the pion coincidence probabilities of obtained data andsimulation in the Λ (I) and Σ (II) regions are almost consistent. However, in the Y ∗ (III)region, they do not always go together. This diﬀerence might be due to the same originof the observed “shift” of Y ∗ peak in the inclusive spectrum.

5.2.2

One-proton coincidence analysis

A proton emitted from the quasi-free processes rarely hits the RCA: only small fractionin the forward segments (Seg1, 4). Moreover, the spectator proton in a deuteron rarely
exceeds the analysis threshold momentum of 250 MeV/c. Therefore, we can expect agood suppression of the quasi-free processes in one-proton coincidence spectrum.
Here, we show the detection eﬃciency of one proton as a function of missing mass
(M Md ) in each segment of RCA in Figure 5.18 produced from a simulation. In thisfigure, the eﬃciency of Λp and Σ0 p final state mode is shown with red and black crosses,
respectively, and the mass threshold of the K − pp system is also shown with a green
line. The detection eﬃciency of the proton gradually increases from the production
threshold of each final state mode and it reaches to an almost flat region. We cansee that the forward (Seg1, 4) and middle (Seg2, 5) segments have an almost flat andwide acceptance with respect to the K − pp mass threshold, although the acceptanceof the backward segments (Seg3, 6) is limited. Therefore, we discuss the one-proton(a): Seg1, 4(b): Seg2, 5-0.22

π d → K W, W → Λp

0.2

π+d → K+ W, W → Σ 0p+(c): Seg3, 6-

K +p+p = 2.37 GeV/c 2-

K +p+p = 2.37 GeV/c 2

+

0.14

+

0.09

0.12

0.16

π+d → K+ W, W → Σ 0p

0.07

0.1

0.06
0.08

1p

1p

0.12
0.1

η

η

1p

+

0.08

0.14

η

π d → K W, W → Λp+π+d → K+ W, W → Σ 0p

0.18

K +p+p = 2.37 GeV/c 2

0.1

π d → K W, W → Λp
+

0.06

0.05
0.04

0.08
0.03

0.04

0.06

0.02

0.04

0.02

0.01

0.02
0
2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.450
2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.450
2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45

MM d [GeV/ c 2]

MM d [GeV/ c 2]

MM d [GeV/ c 2]

Figure 5.18: The detection eﬃciency of a proton for each segment of RCA as a functionof M Md . The eﬃciency for the forward segment (Seg1, 4), the middle segment (Seg2, 5)
and the backward segment (Seg3, 6) is shown in (a), (b) and (c), respectively. The casesof Λp and Σ0 p final state modes are indicated with black and red crosses, respectively.
coincidence spectrum for the middle segments (Seg2, 5) of RCA. Note that there would
be no quasi-free contributions in this spectrum according to the simulation.
Figure 5.19 (b) shows a coincide spectrum with one proton in the middle segments of
RCA and Figure 5.19 (c) shows the coincidence probability spectrum, which was obtained

136

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

by dividing the coincidence spectrum (Figure 5.19 (b)) with the inclusive spectrum (Figure 5.19 (a)). These spectra are without acceptance correction for the RCA. The contamination from the misidentification of π ± in RCA, which is estimated by the side-band
events in P ID described in Sec. 4.4, is shown with hatched spectra in the figure. The
contamination fraction of this component is about 7% around the M Md ∼ 2.27 GeV/c2 .
(a)ΣCounts/(5MeV/c2)

80000
70000
60000
50000
40000

Λ

30000

Y*

20000
10000
0
2

2.1

2.2

2.3

2.4

2.5

MM d [GeV/ c2](b)

Proton coincidence250

π± contamination

200
150
100
50
2.1

2.2

2.3

2.4

2.5

MM d [GeV/ c2]

Coincidence Probability

Counts/(5MeV/c2)

300

0
2

(c)

-

K +p+p = 2.37 GeV/ c 2

0.025
0.02

-

K +p+p = 2.37 GeV/ c 2

Proton coincidence
π± contamination

0.015
0.01
0.005
0
2

2.1

2.2

2.3

2.4

2.5

MM d [GeV/ c2]

Figure 5.19: (a) Inclusive missing-mass spectrum of the d(π + , K + ) reaction. (b) Missingmass spectrum of the d(π + , K + ) reaction with one proton in the middle of the RCA ineach side (Seg2, 5). (c) The coincidence probability of a proton obtained by dividing thecoincidence spectrum (b) with the inclusive spectrum (a). Hatched spectra show the π ±contamination in RCA.
In these spectra, there are possible non-quasi-free contributions of the ΣN thresholdcusp, the K − pp signal emitting through K − pp → Λ(Σ0 )p, and quasi-free hyperons andhyperon resonances productions followed by conversions such as ΣN → ΛN . Here, we
notice there are two prominent structures in Figure 5.19 (c): one at the threshold cusp
position (2.13 GeV/c2 ) and the other broad bump at around 2.27 GeV/c2 , which can be
the signal of the “K − pp”-like structure. In the quasi-free production region of Σ (II) andY ∗ (III), the proton coincidence probability is smaller than the two prominent structuresand stays rather constant.

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

5.2.3

137

Two-proton coincidence analysis

We present the two proton coincidence analysis result, which is also free from the quasifree background. Figures 5.20(b) and (c) show the two-proton coincidence and coincidence probability spectra same as Figure 5.19. At this stage, the acceptance of RCA
is not taken into account. The component of the π ± contamination is also shown withhatched spectra in the figure. The two-proton coincidence probability spectrum also has
the two prominent structures, which are at the threshold cusp position (2.13 GeV/c2 )and the other broad bump at around 2.27 GeV/c2 similar to the one-proton coincidence
probability spectrum.
×10
220
200
180
160
140
120
100
80
60
40
20
0
2

Counts/(15MeV/ c2)

3

(a)

Σ

Λ
Y*
2.1

2.2

2.3

(b)

2.4
2.5
MM d [GeV/ c2]-

K +p+p = 2.37 GeV/ c 2

0.006

Counts/(15MeV/ c2)

2p coincidence300
π± contamination

250
200
150
100
50
0
2

2.1

2.2

2.3

2.4
2.5
MM d [GeV/ c2]

Coincidence Probability

350

(c)

-

K +p+p = 2.37 GeV/ c 2

2p coincidence

0.005

π± contamination

0.004
0.003
0.002
0.001
0
2

2.1

2.2

2.3

2.4
2.5
MM d [GeV/ c2]

Figure 5.20: (a) Inclusive missing-mass spectrum of the d(π + , K + ) reaction. (b) Missingmass spectrum of the d(π + , K + ) reaction with two protons coincidence in RCA. (c) The
coincidence probability of two protons obtained by dividing the coincidence spectrum (b)with the inclusive spectrum (a). Hatched spectra show the π ± contamination in RCA.

5.2.4

Identification of final states in two-proton coincidence

In order to take into account the acceptance of our range counter system, we need
information of the final state of the W in the π + d → K + W reaction. This study was
carried out by requiring coincidence of two protons in the RCA’s.
In order to detect the two protons in our system, the final state of W should be a) Λp,
Λ → pπ − , b) Σ0 p, Σ0 → Λγ → pπ − γ, and c) Y πp → ppππ(γ), where Y is hyperon as Λand Σ. We identified such a final state by measuring the missing-mass squared spectraof X in the d(π + , K + pp)X process by measuring the momenta of two protons in the

138

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

decay of ppX system, of which mass is M Md . In this analysis, the absolute value of the
momenta of protons were obtained from the velocity and emitted angles estimated fromthe vertex position of the (π + , K + ) reaction point and hit position of the first layer of
RCA. The first two modes, a) and b), are non-mesonic and the X is one pion (and γ).
The last one, c), is mesonic and the X is two pions. Therefore, the missing-mass squared
spectrum of MX2 should show diﬀerent distribution for each decay mode.
Figure 5.21 shows such missing-mass squared spectrum of MX2 for each M Md region.
The obtained data is indicated in black points with error bars. These points were shown
after subtraction of the π ± contamination fraction, whose distributions were almost flatin the MX2 . The colored dashed-lines in Figure 5.21 show the Λp, Σ0 p and Y πp final-statecomponents, whose normalization factors were adjusted by a template fit. The total fit
results are also displayed with the black lines.
These templates were made from the simulation, which assumed the reaction of+
π d → K + W, W → pY (pY π) with uniform productions. In the Λp and Σ0 p modes (pY ),we assumed the uniform decay distributions in the center of mass system because theK − pp is considered as spin J = 0. In case of Y πp modes, there are many possible
decay distributions because they are three-body systems. When the K − pp decays to
Y πp modes, the proton momentum in the center of mass system may become small
corresponding to the Fermi momentum in the deuteron [96]. Thus, in the fitting of Figure 5.21, we assumed the weighted decay distribution for the Y πp modes, whose proton’s
momentum was small as the Fermi momentum in the deuteron. Moreover, the templates
for the Y πp modes were made by mixing of the Σ+ π − p, Σ0 π + p and Λπ 0 p components
because the MX2 distributions for such Y πp modes had only small diﬀerences and it isdiﬃcult to distinguish between each other. The mixture ratio was estimated from theelementary cross-section of Y ∗ ’s (see Sec. 5.1.2) and decay branches of Y ∗ ’s to Y π modes.

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

2.10 < MM d < 2.14 [GeV/ c 2 ]2.14 < MM d < 2.18 [GeV/ c 2 ]

90

50

140

50
40

120
100
80

30

60

20

40

10

20
-0.02

0

0.02

CountsCounts60

Counts

60

160

70

0
-0.04

-0.02

0

0.02

0.04

0

0.06

18
16

Counts

12
10
8
6

4
2
0

4
2
0

0.05

Counts

14

6

-0.05

0

0.05

M 2X [(GeV/c 2 )2 ]0.1

2.34 < MM d < 2.38 [GeV/ c 2 ]

-0.05

0

0.05

0.1

0.15

M 2X [(GeV/c 2 )2 ]2.38 < MM d < 2.42 [GeV/ c 2 ]2.42 < MM d < 2.46 [GeV/ c 2 ]
9

12

16

8
10

7

12

8

6

10
8
6

Counts

14

CountsCounts

22
20
18
16
14
12
10
8
6
4
2
0

M 2X [(GeV/c 2 )2 ]

18

6

5
4
3

4

4

2
2

2
0
-0.1

0.02 0.04 0.06 0.08

2.30 < MM d < 2.34 [GeV/ c 2 ]

20

14
12
10
8

0

M 2X [(GeV/c 2 )2 ]2.26 < MM d < 2.30 [GeV/ c 2 ]

22
20
18
16

0

-0.04 -0.02

M 2X [(GeV/c 2 )2 ]2.22 < MM d < 2.26 [GeV/ c 2 ]

-0.05

30

10

0
-0.04

0.04

40

20

M 2X [(GeV/c 2 )2 ]Counts2.18 < MM d < 2.22 [GeV/ c 2 ]

180

80

139

-0.05

0

0.05

0.1

0.15

0

1
-0.1

0

0.1

M 2X [(GeV/c 2 )2 ]0.2

M 2X [(GeV/c 2 )2 ]

0
-0.2

-0.1

0

0.1

0.2

M 2X [(GeV/c 2 )2 ]2.46 < MM d < 2.50 [GeV/ c 2 ]

data

7
6

Total

Counts5π+d → K W, W → Λp+43π+d → K W, W → Σ 0p
+

2
1
0
-0.2

π+d → K W, W → Yπp
+

-0.1

0

0.1

0.2

M 2X

[(GeV/c 2 )2 ]Figure 5.21: Missing-mass squared spectra of X obtained from the two proton coincidence
events in the reaction of the d(π + , K + pp)X. Each spectrum shows the mass square of
X for the diﬀerent M Md region shown in the figure. The spectra were fitted with threecomponents of Λp (red dashed-line), Σ0 p (magenta dashed-line) and Y πp (green dashedline) modes.

140

5.2.5

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

Cross section in two-proton coincidence

The missing mass spectrum is obtained as a double diﬀerential cross section ofd2 σ̄/dΩ/dM averaged over the scattering angle of the (π + , K + ) reaction from 2◦ to 14◦
for the two proton coincidence events1 . We reconstructed the double diﬀerential crosssection only for the Λp and Σ0 p modes because the Y πp modes had the large ambiguities
such as the mixture of each mode and decay distributions. The double diﬀerential crosssection of each final state was calculated as,
NK×2p∑
Br(M Md , MX2 )ij
d2 σ̄2i ◦ –14◦
A
=
,
i
dΩdM
NA (ρx)Nbeam ∆ΩK j=0 ϵπKj η2p(M Md , θπK )j(5.8)

where A is the target mass number, NA the Avogadro constant, ρx the target mass
thickness, Nbeam the number of beam pions on the target, ∆ΩK the solid angle of SKS,ϵπK the overall experimental eﬃciency for the (π + , K + ) measurements same as the ϵ in
Eq. 3.30, NK×2p the number of detected kaons with two protons in the missing-mass interval ∆MX and j indicates the event number. Bri (M Md , MX2 ) is the probability for each
final state estimated from the fitting as in Figure 5.21. The probability Bri (M Md , MX2 )is normalized as,
0BrΛp (M Md , MX2 ) + BrΣ p (M Md , MX2 ) + BrY πp (M Md , MX2 ) + BrContami (M Md ) = 1,
(5.9)
Contami±where Bris the probability of the π contamination in the proton selection region.
iη2p(M Md , θπK ) is the detection eﬃciency of two protons in RCA for each final statecalculated by a Geant4 [91] based Monte Carlo simulation. Figures 5.22 (a) and (b)ishow the detection eﬃciency (η2p
(M Md , θπK )) for the Λp and Σ0 p modes, respectively.
Figure 5.23 is the projection spectra of Figures 5.22. The η2p is almost constant in the
missing mass (M Md ) except near the production threshold. In this analysis, we did not
use the small η2p region to avoid the miss-assignment of the final state. The standard cutoﬀ value was η2p = 0.01, which was about 1/3 of the acceptance in the constant regioni
as shown in Figure 5.23. η2p(M Md , θπK ) was corrected event-by-event by checking the
M Md and scattering angle θπK .

The obtained number of events for the θπK = 14◦ ∼ 16◦ region was small due to the limited
acceptance of the SKS for K + detection. Therefore, we did not use such large scattering angle events
for the coincidence analysis.
15.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION(a) : Λp mode

141(b) : Σ0p mode

16

16

0.035

14

0.04

12

0.035
0.03

10

0.025

8

0.02
0.015

6

θπK(Lab) [degree]

θπK(Lab) [degree]

0.045

14

0.03

12

0.025

10

0.02

8

0.015

6

0.01

4

0.005

0.01

4

0.005

2

2.1

2.2

2.3

2

0

2.4

2.1

MM d [GeV/c2]

2.2

2.3

2.4

0

MM d [GeV/c2]

Figure 5.22: Detection eﬃciency of two protons η 2p for Λp and Σ0 p modes are shown in(a) and (b), respectively. The eﬃciency was corrected event-by-event by checking the
M Md and θπK .

(a) : Λp mode(b) : Σ0p mode
0.05

0.04

0.04

0.03

0.03
2p

0

2p

ηΛp

ηΣ p

0.05

0.02

0.02

0.01

0.01

0

2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45

MM d

[GeV/c2]0

2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45

MM d [GeV/c2]

Figure 5.23: Detection eﬃciency of two protons η 2p for Λp (a) and Σ0 p (b) modes as afunction of M Md . These are the projection spectra of Figure 5.22.

142

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

Figure 5.24 (a) and (b) show the obtained double diﬀerential cross section (d2 σ̄/dΩ/dM ) averaged over the scattering angle from 2◦ to 14◦ for the Λp andΣ0 p modes, respectively. The errors in those spectra were determined by the statisticalerror of two-proton coincidence events (NK×2p ). They also include the ambiguity of thefraction of π ± contamination (BrContami in Eq. 5.9), and the statistical error of the final
state determination (Bri in Eq. 5.8) shown in Figure 5.21.
(a): Σp moded σ /d Ω/dM 2o-14o(Lab) [µb/sr/(15MeV/c 2)]

4
3.5
3
2.5
2
1.5
1
0.5
0
2

2

2

d σ /d Ω/dM 2o-14o(Lab) [µb/sr/(15MeV/c 2)](a): Λp mode
4.5

2.1

2.2

2.3

2.4
2.5
2.6
MMd [GeV/c 2]

0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
2

2.1

2.2

2.3

2.4
2.5
2.6
MMd [GeV/c 2]

Figure 5.24: The double diﬀerential cross section for the Λp (a) and Σ0 p (b) final statemodes estimated from the fitting of MX2 as shown in Figure 5.21. These spectra are
obtained from the two-proton coincidence events.

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

5.2.6

143

Results on proton coincidence spectra

We have observed a broad enhancement in the Σ0 p spectrum as shown in Figure 5.24 (b).
Here, we call the obtained broad enhancement as a “K − pp”-like structure. In this Σ0 p
spectrum, there is no considerable background processes. On the other hand, in the Λpspectrum in Figure 5.24 (a), there is a large component around 2.13 GeV/c2 , while thecomponent around 2.28 GeV/c2 corresponding to the “K − pp”-like structure is also seen.
Therefore, we did not use Λp spectrum for the fit to evaluate the mass and width of the“K − pp”-like structure. The large component around 2.13 GeV/c2 is interpreted as theΣN cusp and the conversion process of ΣN → Λp reaction. The detail discussion forthis component in the Λp spectrum is described in Appendix C.
We fitted the Σ0 p spectrum to evaluate the mass and width of the “K − pp”-likestructure with a relativistic Breit-Wigner function as,f (M Md ) =(2/π)M Md m0 Γ(q).
2
(m0 − M Md2 )2 + (m0 Γ(q))2(5.10)(a): Λp mode
4.5
4
3.5
3
2.5
2
1.5
1

0

2

0.5

d σ / d Ω/ dM 2o-14o(Lab) [µb/sr/(15MeV/c2)]2d σ / d Ω/ dM 2o-14o(Lab) [µb/sr/(15MeV/c2)]

The mass-dependent width was Γ(q) = Γ0 (q/q0 ), in which q (q0 ) is the momentum ofthe Σ0 and proton in the Σ0 p rest frame at mass M Md (m0 ). Note that we did not use
the Λp spectrum for the evaluation of the mass and width of the “K − pp”-like structure.
Figure 5.25 (b) shows the fit result of the Σ0 p spectrum with the relativistic Breit-Wigner
function.

2

2.1

2.2

2.3

2.4

2.5

MM d

2.6

[GeV/c2](b): Σ0p mode
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

2

2.1

2.2

2.3

2.4

2.5

2.6

MM d [GeV/c2]

Figure 5.25: The double diﬀerential cross section for the Λp (a) and Σ0 p (b) final statemodes fitted with the relativistic Breit Winger function. These cross section spectra aresame as Figure 5.24. The solid lines and dashed lines show the obtained relativistic Breit
Wigner function of the fitted region and whole region, respectively. The evaluation of
the mass and width was carried out only using the Σ0 p spectrum. The determination of
the branching fraction of the “K − pp”-like structure was carried out by fitting with theΛp and Σ0 p spectra with the common parameters assuming the same mass distributionof M Md . (b) is taken from Ref. [112].

144

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

The mass, width and these statistical errors were estimated from the χ2 distributionof the fit as a function of the mass (m0 ) and width (Γ0 ) of the “K − pp”-like structure
shown in Figure 5.26. The χ2 -determination scheme is same as the one for the ΣN -cusp
analysis (Figure 5.11). The mass and width of the “K − pp”-like structure were found to+87
2
be 2275 +17−18 (stat.) MeV/c and 162 −45 (stat.) MeV, respectively. It corresponds to thebinding energy of the K − pp system to be 95 +18−17 (stat.) MeV.

Γ0 [MeV]

χ2

280
260

22

240

20

220

18

200

16

180

14

160

12

140

10

120

8

100

6

2250

2260

2270

2280

2290

2300

m0 [MeV/ c2]

Figure 5.26: The contour plot of the χ2 of the fitting as a function of the mass (m0 ) andwidth (Γ0 ) of the “K − pp”-like structure. The black lines show ∆χ2 = +1, +2 and +3
regions from the minimum χ2 value shown in a cross. The red lines show the 1σ and 2σdeviations.
Next, we estimated the systematic uncertainty of the mass and width for the “K − pp”like structure. The systematic error of the width is larger than the one for the mass sameas the statistical error. In this analysis, we identified the final state in two-proton coincidence by fitting with the template functions of the missing-mass squared MX2 of thed(π + , K + pp)X reaction. In order to estimate the uncertainty of the final state determination method, we carried out the template fit with not only the MX2 spectrum but
also missing-energy (EX ) spectra. The uncertainties of the width and mass originatingfrom this ambiguity were 61 MeV and 9 MeV/c2 , respectively. This uncertainty is thelargest component of the systematic error. The analysis using the EX spectra is described in Appendix D. Moreover, since we used the template fit to identify the final
state, the shape of the mass distribution might be changed when we used the diﬀerent
templates from diﬀerent assumptions. Since the Λp and Σ0 p modes are two body systems, we have less assumptions to make the templates. On the other hand, we madethe Y πp templates with diﬀerent assumptions of the decay distributions and mixture
ratio for each component. In this analysis, we assumed the weighted decay distributions,whose proton’s momentum was small as the Fermi-motion in the deuteron, for the Y πp
modes. In order to estimate the systematic error of this assumption, we changed the
decay distribution to the three-body phase-space distribution. The systematic errors of
the width and mass of this ambiguity were 33 MeV and 10 MeV/c2 , respectively. We

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

145

also changed the diﬀerent mixture ratio for the Y πp modes. In the simulation, we madethe Y πp template functions by mixing of the Σ+ π − p, Σ0 π 0 p and Λπ 0 p components according to the elementary cross-section of Y ∗ ’s. We carried out another template fit bychanging the Y πp mixed template to single Λπ 0 p and Σπp (Σ+ π − p : Σ0 π 0 p = 1 : 1)
templates to estimate the ambiguity from this assumption. The systematic errors of
the width and mass of this assumption were 25 MeV and 2 MeV/c2 , respectively. We
also estimated the ambiguity originating from the fitting function. For this estimation,
we performed the mass fit using the Lorentzian function instead of the relativistic Breit
Wigner function. The systematic errors of the width and mass originating from thisuncertainty were 19 MeV and 3 MeV/c2 , respectively. The ambiguities originating fromthe binning and fit region were 20 MeV (width) and 9 MeV/c2 (mass). The systematic
uncertainty of each component is shown in full width. Finally, the mass and width of+21
2
the “K − pp”-like structure were estimated to be 2275 +17−18 (stat.) −30 (syst.) MeV/c and+87+66
162 −45 (stat.) −78 (syst.) MeV, respectively. It corresponds to the binding energy of the+30
K − pp system to be 95 +18−17 (stat.) −21 (syst.) MeV.
The production cross section of the “K − pp”-like structure decaying to Σ0 p was estimated from the fit of the Σ0 p spectrum by using the evaluated mass and width of the“K − pp”-like structure. The evaluated production cross section was dσ/dΩK − pp→Σ0 p =3.0 ± 0.3 (stat.) µb/sr. A branching fraction of the “K − pp”-like structure of ΓΛp /ΓΣ0 p
was estimated by fitting the Λp and Σ0 p spectra with the common parameters as shownin Figure 5.25 (a) and (b), respectively. The mass distribution of the Λp mode wasassumed to be same as the Σ0 p one. Here, the Λp spectrum has the large component
around 2.13 GeV/c2 corresponding to the ΣN cusp and ΣN → Λp conversion. Thus, we
did not use such low missing-mass region of the Λp spectrum for the fit. We evaluatedthe branching fraction to be ΓΛp /ΓΣ0 p = 0.92 +0.16−0.14 (stat.).
For the production cross section and the branching fraction, we also estimated thesystematic error. The origins of these systematic error were almost same as the ones
for the mass and width. The systematic errors caused from the final state determinations, which was estimated by changing the fitting spectrum to EX , were obtained
to be 0.7 µb/sr for the production cross section and 0.21 for the branching fraction.
The uncertainties originating from the assumption of the decay distributions of the Y πp
modes were 0.8 µb/sr (dσ/dΩK − pp→Σ0 p ) and 0.42 (ΓΛp /ΓΣ0 p ). The systematic errors
originating from the assumption of the mixture ratios of the Y πp modes were foundto be 0.1 µb/sr (dσ/dΩK − pp→Σ0 p ) and 0.17 (ΓΛp /ΓΣ0 p ). In case of the systematic-error
estimation of the diﬀerential cross section and the branching fraction, we did not take
into account the ambiguity of the fit using the Lorentzian function. Moreover, we estimated the systematic error caused from the uncertainties of the mass and width bychanging these values within the evaluated errors. These systematic uncertainties were0.1 µb/sr (dσ/dΩK − pp→Σ0 p ) and 0.33 (ΓΛp /ΓΣ0 p ). The systematic uncertainty of eachcomponent is also shown in full width. Finally, we evaluated the production cross section and the branching fraction to be dσ/dΩK − pp→Σ0 p = 3.0 ± 0.3 (stat.) +0.7
−1.1 (syst.) µb/sr+0.16
and ΓΛp /ΓΣ0 p = 0.92 −0.14(stat.) +0.60(syst.),
respectively.
Furthermore,
there is addi−0.42+1.3
tional uncertainty for the diﬀerential cross section dσ/dΩK − pp→Σ0 p of −0.0 µb/sr arisingfrom the discrepancy of the proton detection eﬃciency of the p(π + , K + )Σ+ analysis as
described in Sec. 4.5.

146

5.2.7

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

Discussion on proton coincidence spectra

1.6
Y*Inclusive

1.4"K pp" → Σ0p

1.2"K pp" → Λp

-

-

×0.1

1
0.8
0.6
0.4

Σ
Λ

0.2

2

d σ /d Ω/dM 2o-14o(Lab) [µb/sr/(MeV/c2)]

We compare the “K − pp”-like structure with the elementary cross sections. A comparison of the double diﬀerential cross sections between the inclusive and “K − pp”→ Σ0 (Λ)pspectra is shown in Figure 5.27. A diﬀerential cross section of the Y ∗ region (Region I
II) of the inclusive spectrum is evaluated to be dσ/dΩY ∗ = 168.6 ± 6.3 µb/sr. Here,the elementary diﬀerential cross section of the Λ(1405) production was found to be
36.9 ± 1.8 µb/sr, which was measured in Ref. [19]. Thus, the production probabilitiesof the “K − pp”-like structure, which decays to Σ0 p mode, for the inclusive diﬀerential
cross section of the Y ∗ region and the elementary diﬀerential cross section of Λ(1405)
are found to be (dσ/dΩK − pp→Σ0 p )/(dσ/dΩY ∗ ) = 1.8 ± 0.2 (stat.) +0.4
−0.7 (syst.) % and+1.9(dσ/dΩK − pp→Σ0 p )/(dσ/dΩΛ(1405) ) = 8.2 ± 1.0 (stat.) −3.0 (syst.) %. These values correspond to the probabilities of the “K − pp”→ Λp mode of about 1.6% for the dσ/dΩY ∗and about 7.5% for the dσ/dΩΛ(1405) . Since we only measured the mass spectra of the“K − pp”-like structure for the Σ0 p and Λp modes, we can evaluate the lower limit of
the sticking probability of the Λ(1405)p →“K − pp” reaction to be ≳ 15.7%, where weassume the “K − pp”-like structure can be produced only from the Λ(1405) doorway process. This lower limit of the sticking probability is large compared with a theoreticalvalue about 1% [69]. This discrepancy might originate from the incorrect assumptionthat the K − pp bound state is formed through the Λ(1405) doorway K − pp formation as
the Λ(1405) doorway and/or the nature of “K − pp”-like structure, which might be not
the simple K − pp bound state but the other possibilities like a dibaryon as πΛN –πΣNbound states [2], a Λ∗ N bound states [3], and a lower πΣN pole of the K − pp [113].

0

2.1

2.2

2.3

2.4
MM d [GeV/c2]

Figure 5.27: Comparison of the double diﬀerential cross sections between the inclusive
spectrum and “K − pp”-like structure. The black crosses show the obtained inclusive
spectrum. The red line and green dashed-line show the mass spectrum of the “K − pp”like structure, which decays to the Σ0 p and Λp modes respectively. In the M Md <2.22 GeV/c2 region, these spectra were multiplied by 0.1.

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

147

Next, we try to understand the coincidence probability spectrum of the one-proton
coincidence analysis shown in Figure 5.19 (c) with the evaluated K − pp mass distributionof f (M Md ). By using the mass distribution for the “K − pp”-like structure and thed2 σ
double diﬀerential cross section of the inclusive (π + , K + ) process dΩdM
(M Md )Inclusive
Md
shown in Figure 5.1 (b), we can obtain the coincidence probability spectrum as shownin Figure 5.28 as a plot colored in magenta, which is calculated as,
Rp (M Md ) =C × f (M Md ) × η1p (M Md ),d2 σ
( dΩdM(M
M))
dInclusvieMd(5.11)

Coincidence Probability

where C is the normalization constant, and η1p (M Md ) is the detection eﬃciency of a
proton in the middle segments of the RCA (Seg2, 5) shown in Figure 5.18 (b). A blue line
in Figure 5.28 is an assumed flat component representing the conversion processes and theπ ± contamination due to the misidentification of π ± in RCA. Red points with error bars in
Figure 5.28 are the sum of the magenta points and blue line. The normalization constant
C and the amplitude of the flat component (blue line) were adjusted to minimize thediﬀerences between the black and red points. Thus, the obtained one proton coincidence
probability spectrum of the broad enhanced region could be reproduced by the “K − pp”
and flat background.

0.025
0.02

Proton coincidence

π± contimination

0.015
0.01
0.005
0
2

2.1

2.2

2.3

2.4

2.5

MM d [GeV/c2]

Figure 5.28: The one proton coincidence probability spectrum of the middle segment of
RCA same as Figure 5.19 (c) with the interpreted spectrum shown in colored spectra.
A magenta spectrum was obtained from the Eq. 5.11 corresponding to the componentof the “K − pp”-like structure. A blue line indicated the flat component representing theconversion processes and π ± contamination. Red points with error bars are the sum of
the magenta points and blue line.

148

CHAPTER 5. EXPERIMENTAL RESULTS AND DISCUSSION

What is the nature of the “K − pp”-like structure?
Since we used the
π d → K + “K − pp”, “K − pp” → Σ0 (Λ) p reaction, the “K − pp”-like structure should
be strangeness −1 and baryon number B = 2, so that the hyper charge Y = 1. The
K − pp is theoretically considered as the J P = 0− , where a K − couple with a spin-singlet(S = 0) p-p pair in S-wave (L = 0). The possible theoretical interpretation as a Λ∗ pbound state also predicted to be J P = 0− for the bound state [3]. There is also a theoretical prediction of a dibaryon as πΛN –πΣN bound state, whose quantum number is(Y, I, J P ) = (1, 3/2, 2+ ) [2]. However, from the isospin point of view, the isospin of thesystem should be 1/2 not 3/2, because we have observed the Λp mode.
+250

ΓK - pp [MeV]200This data

150
DISTO
N.V.Shevchenko, A.Gal, J.Mares

100 A. Dote, T.Hyodo, W.Weise

Y.Ikeda, T.Sato
T.Yamazaki, Y.Akaishi

50 N.Barnea, A.Gal, E.Z.Liverts

FINUDAOBELIX

S.Wycech, A.M.Green
Y.Ikeda, H.Kamano, T.Sato

0

0

20

40

60

80

100 120 140
BK - pp [MeV]

Figure 5.29: Comparison of the binding energy and width of the K − pp. The calculated
binding energy and width using the chiral SU(3)-based energy dependent potentials areshown with circles and the ones calculated with the energy independent potentials areindicated with triangles (same as Figure 1.15). The experimental values evaluated fromthe FINUDA [43], DISTO [46] and OBELIX [49] experiments are indicated with red
squares. The values obtained from this data are shown with a magenta square. For theexperimental values, the statistical and systematic errors are shown with the blue andgreen lines, respectively.
Our obtained mass corresponding to the K − pp binding energy of about 100 MeV
and broad width are not inconsistent with the values evaluated from the FINUDA andDISTO experiment within the error as shown in Figure 5.29. However, theoretical calculation for the K − pp is diﬃcult to reproduce such a deep binding energy about 100 MeV.
In this view, recently Maeda, Akaishi and Yamazaki reported an interesting study [114].
They studied some kaonic nuclei such as the K − pp with the phenomenological K̄N potential [1, 40] using the Faddeev and Faddeev-Yakubovsky method. They conducted
an analysis on the eﬀect of the partial restoration of chiral symmetry on the K̄N interaction on the basis of the “clearing QCD vacuum” model of Brown, Kubodera andRho [115]. Finally, they pointed out that the renormalized interaction strength of K̄N
system due to the partial restoration of the chiral symmetry can reproduce such a large
K − pp binding energy about 100 MeV. There is also an interesting theoretical study,

5.2. COINCIDENCE ANALYSIS: RESULTS AND DISCUSSION

149

which was reported by Dóte, Inoue and Myo recently [113]. They proposed a new calculation method where the coupled-channel complex scaling method and the Feshbach
projection were combined, and applied it to the K − pp system. The evaluated binding energy of the K − pp using the chiral SU(3)-based energy dependent potential was
about 27 MeV. On the other hand, when they calculated using NRv2c potential (one of
the chiral SU(3)-based energy dependent potentials) they always obtained another quasi
self-consistent solution corresponding to the K̄N N resonance near the πΣN threshold,which was equivalent of the K − pp binding energy of about 100 MeV, with large decay
width. Those quasi-consistent solutions are considered as related to the lower pole ofΛ(1405), while the solutions described above must be related to the higher pole. In otherwords, the K − pp might have the double pole structure as same as the Λ(1405). These
theoretical suggestions seem to be interesting to understand the obtained “K − pp”-likestructure.
The branching fraction of the K − pp bound state of ΓΛp /ΓΣ0 p was discussed from atheoretical point in Ref. [116]. In this paper, it was found that the branching fractionof these modes strongly depends on the ratio between the couplings Λ(1405)-K̄N andΛ(1405)-πΣ. A larger Λ(1405)-K̄N coupling leads to an enhancement of Λp decay mode.
Furthermore, this ratio was predicted to be ΓΛp /ΓΣ0 p ∼ 1.2 using the chiral unitary
approach. The predicted value is not in-consistent with the obtained value within theerror.
In the next step, further experiment with high statistics and a larger acceptance detector system is important to reduce both statistic and systematic errors and improve
the sensitivities for the “K − pp”-like structure. One of the detector systems to carry out
the further experiment using the same reaction is large-acceptance Hyperon spectrometer with TPC (HypTPC) to detect the decay particles and KURAMA spectrometer
to measure the K + momenta [117]. This detector system will be used by the J-PARC
E42 experiment to search for the H-dibaryon at J-PARC K1.8 beam line [117]. Since
HypTPC (∼2π) and KURAMA spectrometer (∼200 msr) have the large acceptance, wewill be able to improve the statistics more than 10 times than the present experiment.
Moreover, we will be able to obtain not only the missing-mass spectrum but also theinvariant-mass spectra because HypTPC can measure the momenta of the decay charged
particles with the magnetic system. Thus, we can measure not only the non-mesonic decay modes such as Λp and Σ0 p but also the mesonic (Y πp) decay modes. In addition,
we can search the origin of the obtained “shift” of the Y ∗ region by reconstructing theinvariant-mass spectrum. After we establish the “K − pp”-like structure in this detector
system, we are going to search the further systems such as K − ppp and K − K − pp by using
the 3 He(π + , K + ) and d(K − , K 0 ) reactions.

Chapter 6
Conclusion
The strange dibaryon systems (S = −1, B = 2) beyond the octet baryon pair (ΛN , ΣN )are experimentally not well explored, yet. A recently interested system of K̄N N is suchan example. Theoretically a bound state of K − pp is expected to exist, but maybe abroad resonance. However, the experimental status is still not conclusive although someexperimental evidences are reported.
In order to improve the situation, we have newly investigated the strange dibaryon
system with the d(π + , K + ) reaction at the pion incident momentum of 1.69 GeV/c. The
reaction can produce a broad energy range of excitation spectrum from Λ, Σ hyperons toΛ(1405), Σ(1385) excited hyperon resonances as well as K̄N . The involved elementary
processes of the π + + p/n reactions are rather well known at this energy, so that we canfully explore exotic states in the wide energy range.
The J-PARC E27 experiment was carried out at the K1.8 beam line of the hadronexperimental hall at J-PARC to search for the K − pp bound state by using the d(π + , K + )reaction at 1.69 GeV/c. In this reaction, the K − pp is expected to be formed through theΛ(1405) production as a doorway [69]. In this experiment, we measured the missing-mass
spectrum of the d(π + , K + ) reaction by analyzing the incident beam π + and emitted K +momenta. Furthermore, the coincidence measurement was also performed by detecting
proton(s) in order to suppress the quasi-free hyperon production processes.
We obtained the inclusive missing-mass spectrum at the laboratory scattering angle between 2◦ and 16◦ in high statistics and high energy resolution for the first time.
The present data cover a wide missing-mass range from the Λ production thresholdto the Λ(1405)/Σ(1385) region. The overall structure was understood with a simple
quasi-free picture based on the known elementary processes. However, there were two
peculiar deviations from this picture. One observation is the ΣN cusp, of which mass
was found to be 2130.5 ± 0.4 (stat.) ± 0.9 (syst.) MeV/c2 with the width of Γ =+0.6
5.3 +1.4−1.2 (stat.) −0.3 (syst.) MeV. The peak position is consistent with previous measurements. Further detailed theoretical studies including the present data would reveal theinformation on the ΣN -ΛN coupling strength and the pole position. Another observationis that the centroid of the broad bump structure in the Y ∗ production region was significantly shifted to low mass side as compared with a simple quasi-free simulation, by about+2.7
2
32.4 ± 0.5 (stat.) +2.9
−1.7 (syst.) (22.4 ± 0.4 (stat.) −1.7 (syst.)) MeV/c for M Md (M Mp )spectra. In order to clarify the origin of the peak shift, further experiments to measure
150

151
not only the missing-mass spectra but also invariant-mass spectra and theoretical studies
are necessary.
We have measured the missing-mass distributions of d2 σ̄/dΩ/dM in the π + d →+K W, W → Σ0 (Λ)p reactions in the scattering angle between 2◦ and 14◦ for the firsttime. Here, the final states of Σ0 p and Λp were identified using the missing-mass squared
MX2 distribution of d(π + , K + pp)X reaction by measuring the two protons in the RCA. A
broad enhancement have been observed in the missing-mass distribution of the Σ0 p modearound 2.27 GeV/c2 corresponding to the “K − pp”-like structure. The mass and width+21
2of the “K − pp”-like structure were evaluated to be 2275 +17−18 (stat.) −30 (syst.) MeV/c+87+66
and 162 −45 (stat.) −78 (syst.) MeV, respectively, by fitting with the relativistic Breit
Wigner function. These obtained mass and width are not inconsistent with the values evaluated from the FINUDA and DISTO experiments within the errors, although
our statistical and systematic errors are large. If the observed structure originatesfrom the K − pp bound state, the binding energy of the K − pp system corresponds to+30
be 95 +18
−17 (stat.) −21 (syst.) MeV. Such a large binding energy together with a large
width is diﬃcult to reproduce in the present theoretical models. The other possibilities
like a dibaryon as πΛN –πΣN bound states [2], a Λ∗ N bound states [3], and a lower πΣNpole of the K − pp [113] might be considered as alternatives. In this view, the isospin of
the “K − pp”-like structure should be 1/2 not 3/2, while a dibaryon as πΛN –πΣN boundstate [2] is expected to be isospin I = 3/2. Furthermore, we have measured the branching fraction between the Λp and Σ0 p decay modes of the “K − pp”-like structure to be+0.16
ΓΛp /ΓΣ0 p = 0.92 −0.14(stat.) +0.60−0.42 (syst.), for the first time. The obtained branching fraction is not in-consistent with the theoretically predicted value of ΓΛp /ΓΣ0 p ∼ 1.2 [116]using the chiral unitary approach within the error, although our error is large. In orderto reduce these errors, further experiments with higher statistic and larger acceptancedetector system is important.

152

CHAPTER 6. CONCLUSION

Acknowledgements
I would like to express my sincere gratitude to Prof. Tomofumi Nagae who is my supervisor and the spokesperson of the present experiment. He suggested me to join theexperiment and gave me the opportunity to write this doctoral thesis. He always encouraged me and gave me the fruitful suggestions. The discussions with him are theirreplaceable treasure for me. But for his shrewd advice and helpful suggestions, I would
have never been able to complete this work.
During doctor course, I belong to the “Research Group for Hadron Physics” at Advance Science Research Center (ASRC) of Japan Atomic Energy Agency (JAEA). I
would like to deeply acknowledge Prof. Ken’ichi Imai, who is a leader of this group andsuggested me to join this group. He always helped me when I was in trouble. His warm
advice and sharp insight for physics were quite helpful for me.
I would like to express my thanks to Dr. Hiroyuki Fujioka. He always gave mecomments about data analyses and physics. I have learned various things from him andthey will help me in my life as a physicist.
I would like to thank the J-PARC E27 collaborators and all the people who worked
with me. In particular, I am grateful to Dr. Atsushi Tokiyasu, who was my colleague atthe graduate school. He gave me the first instruction on the experimental techniques.
Moreover, I would like to thank Mr. Hiroyuki Ekawa. He worked hardly to construct
and install the RCA for the present experiment. Without his eﬀorts, it is diﬃcult to succeed the present experiment. I also acknowledge Dr. Kotaro Shirotori and Mr. Tomonori
Takahashi, who were pioneers of J-PARC K1.8 beam line groups. I have learned many experimental techniques and analysis methods from them. I wish to acknowledge Dr. Ryuta
Kiuchi, Prof. Takeshi Koike, Dr. Koji Miwa, Prof. Atsushi Sakaguchi, Prof. Hirokazu
Tamura, Prof. Kiyoshi Tanida, and Dr. Mifuyu Ukai. They gave me fruitful advice andsuggestions based on their profound knowledge and experience. I also thanks Mr. Shuhei
Hayakawa, Dr. Ryotaro Honda, Mr. Changwoo Joo, Mr. Yuki Matsumoto, Mr. Ryosuke
Ota, Mr. Toshiyuki Tanaka, Mr. Takeshi Yamamoto, and Mr. Seongbae Yang. I owed
the success of the present experiment to their strong help. Moreover, I could enjoy mylife with them at J-PARC.
I have spent my graduate school days as a member of the “Experimental Nuclear
and Hadron Physics Laboratory (NH)” in Kyoto University. I would like to acknowledge
Prof. Takahiro Kawabata, Prof. Megumi Naruki, Dr. Tetsuya Murakami, Dr. Masayuki
Niiyama, and Dr. Toshiyuki Gogami for the help and encouragement. I wish to express
my thanks to Dr. Manabu Moritsu, Mr. Shunsuke Kanatsuki, Mr. Nobuaki Amano and
Mr. Kohei Takenaka. I worked at K1.8 beam line and enjoyed the experiment with them.
I have also belonged to the “Research Group for Hadron Physics” in JAEA during the doctor course. I am grateful to Prof. Hiroyuki Sako, Prof. Toshiki Maruyama,
Prof. Shoichi Hasegawa, Prof. Susumu Sato, Dr. Hwang Sanghoon, and Dr. Kenji Hosomi
to give me warm advise. I also wish to thank Dr. Hitoshi Sugimura and Dr. Tong-Gyu
Lee. I enjoyed the discussion and spent good days with them in Tokai.
I have joined two experiments, J-PARC E19 and E10 experiments, which were carriedout at J-PARC K1.8 beam line. I acknowledge all the members of J-PARC E19 and E10collaborations.

153
The present experiment was successfully carried out owing to the staﬀs of J-PARC
and KEK. I would like to thank the Hadron beam channel group, accelerator group,and cryogenics section in J-PARC for their great eﬀorts on stable machine operation
and beam quality improvement. Especially, I would like to acknowledge Prof. Toshiyuki
Takahashi and Prof. Masaharu Ieiri to plan the schedule of beam time. Moreover, I would
like to thank Prof. Shigeru Ishimoto and Prof. Shoji Suzuki for the stable operation of
the liquid hydrogen and deuterium target.
Finally, but not the least, I want to express my best thanks to my parents, Keiichiro
Ichikawa and Junko Ichikawa. Their supports throughout my 28 years life led my dreamcome true.

Appendix A
BH1 filter tracking
In finding the BC1, 2 track, we applied the hit position gate for each layer by checking
consistency of hit position with the BH1 hit segment (BH1Filter) as Figure A.1. When
there were multi-hits in BH1 segment, the true hit segment which has the proper timing
was selected by requiring the least |Beam TOF| segment. For example, the hits within
the red lines in Figure A.1 were included to the track candidates. Figure A.2 shows the
typical hit position gate for BH1Filter. In this case, it is shown that the hit position
gate of BC1-X layer with the BH1 Seg5 hit. Moreover, the hit profile of this layer under
the low rate (∼10k pion/spill) and the high rate (∼3.5M pion/spill) beam condition are
also shown in the black and red line, respectively. Here, the black and red spectrum was
required the single hit in BH1 Seg5 and at least one hit in BH1 Seg5, respectively. Thus,
the BH1Filter helps to search the true track which made the trigger with a good time
resolution of BH1, 2 and improve the single track eﬃciency.

154

155

BH1
× Included to track candidates

× Excluded to track candidates

×
×

×
×

×
×

×
×

×
×

×
×

×
×

BC1

×
×

×
×

×
×

×
×

×
×

BC2

Accidental
True timming

Figure A.1: Schematic view of BH1Filter. The hits within the red line gate were included
to the track candidates.

1400
Gate for tracking
1200

Counts1000
low rate (nhBH1=1)

800
600

3.5M pion/spill

400
200
0

-40

-20

0

20

40

60

80

100

Hit profile of BC1 layer
Figure A.2: Typical hit position gate of BH1Filter tracking. The hit profile of BC1-X
layer of each condition is also shown. See the text for the detail.

Appendix B
Accuracy of time oﬀset of RCA
The time oﬀset for each segment of RCA was adjusted by using the π + peak fromthe Σ+ → π + n decay in the π + d → K + Σ+ X reaction described in Sec. 4.2. The
accuracy of the time-oﬀset adjustment was studied by using the two protons coincidence event. As described in Sec. 5.2.4, when we select the missing-mass region of
2.1 < M Md < 2.22 GeV/c2 , the almost all component of the final state of the W inthe π + d → K + W reaction should be Λp. Thus, the mass-square spectrum of MX2 of thed(π + , K + pp)X reaction of this missing-mass region should sit on the π − region.
In this study, we additionally applied the time oﬀset of (−0.30, −0.15, +0.15,+0.30) ns and compared the peak position of the MX2 spectrum for each time oﬀset
condition with the simulated spectrum. Figure B.1 (a, b, c, d, e) show the obtained
MX2 spectrum for the missing-mass region of 2.1 < M Md < 2.22 GeV/c2 with theadditional time oﬀset of (−0.30, −0.15, 0.00, +0.15, +0.30) ns, respectively. The peak
position of the MX2 spectrum for each time-oﬀset condition was evaluated by fitting with
the Gaussian function as shown in red lines in Figure B.1. Thus, the peak position of
the MX2 spectrum decreases as the time-oﬀset parameter is increased. The simulated
MX2 spectrum for the Λp final state mode is shown in Figure B.1 (f). The obtained
peak position for each time oﬀset condition is summarized in Figure B.1 (g), where thepeak position of the simulated spectrum is indicated with the black line. Therefore, theobtained peak position of the MX2 spectrum without additional time-oﬀset parameteris consistent with the simulation within the error bar. Moreover, we found that theaccuracy of the time-oﬀset parameter of RCA was less than 0.1 ns.

156

157

(a): Time offset = -300 ps
250

Counts

200
150
100
50
0

-0.05

0

0.05

2

MX [GeV/ c 2 ](b): Time offset = -150 ps
250Counts

200
150
100
50
0

-0.05

0

(c): Time offset =

0.05

2

MX [GeV/ c 2 ](g): Summary of the peak position

0 ps

150
100
50
0

-0.05

0

0.05

2

MX [GeV/ c 2 ](d): Time offset = +150 ps
200Counts

150
100

Peak position [GeV/c2 ]Counts

200

0.03

0.025

0.02

0.015
50

-0.3
0

-0.05

0

0.05

2

MX [GeV/ c 2 ]

-0.2

-0.1

0

0.1

0.2

0.3

Time offset [ps](e): Time offset = +300 ps

Counts

150
100
50
0

-0.05

3

×10

0

0.05

2

MX [GeV/ c 2 ](f): Simulation

300

Counts

250
200
150
100
50
0

-0.05

0

0.05

2

MX [GeV/ c 2 ]Figure B.1: (a, b, c, d, e) The obtained MX2 spectrum for the missing-mass region of
2.1 < M Md < 2.22 GeV/c2 with the additional time oﬀset of (−0.30, −0.15, 0.00,+0.15, +0.30) ns. (f) The simulated MX2 spectrum for the Λp final state mode. These
spectra was fitted with the Gaussian function as the red lines. (g) The summary of thepeak position of MX2 spectrum obtained from the Gaussian fitting for each time-oﬀset
condition. The peak position of the simulated spectrum is shown with the black line.

Appendix CΣN cusp for two-proton coincidence
analysis
The obtained double diﬀerential cross section of the Λp final state mode evaluated fromtwo-proton coincidence events has a large component around 2.13 GeV/c2 as shown in
Figure 5.24 (a). It is interpreted as the ΣN cusp and the conversion process of ΣN → Λp.
Figure C.1 (α) show an enlarged view around 2.13 GeV/c2 when we select the forward
scattering angle of θπK(Lab) = 2◦ –8◦ . Note that the Λp spectrum around 2.13 GeV/c2
does not depend on the final state identification because almost all of the component
around this low missing-mass region is Λp mode.
In Figure C.1 (α), we notice two prominent components as the ΣN cusp and theconversion process of ΣN → Λp. We fitted with the Lorentzian function folded with theresolution of 1.4 MeV/c2 in σ for the cusp (green line) and a Gaussian function for theΣN → Λp conversion (blue line). The total fitting function is also shown in a red line.
In this fitting, the parameters of the Lorentzian function of the peak position and thewidth as well as the diﬀerential cross section (dσ/dΩ) were set as the values obtained
from the fitting of the inclusive spectrum described in Sec. 5.1.3. Thus, the ΣN cusp
signal in two-proton coincidence analysis can be understood by the result of the inclusive
analysis.
The similar structure, ΣN cusp and ΣN → Λp conversion, was observed a past experiment [109]. In this experiment, they also used the d(π + , K + ) reaction, although theincident beam momentum was 1.4 GeV/c (our beam momentum is 1.69 GeV/c). They
measured the missing-mass spectrum using the magnetic spectrometer with the multiplicity counter surrounding the deuterium target. The observed missing-mass spectra byrequiring the multiplicity 1, 2 and 3 are shown in Figure C.1 (a), (b) and (c), respectively. The spectra with multiplicity 1 and 3 (Figure C.1 (a) and (c)) can compare with
our inclusive and two proton coincidence Λp spectrum, respectively. The missing-mass
distributions, which corresponds to be ΣN cusp and ΣN → Λp conversion, between ourΛp spectrum (Figure C.1 (α)) and their multiplicity 3 spectrum (Figure C.1 (c)) aresimilar. Thus, we consider that our obtained Λp spectrum around this low missing-mass
region is reasonable.

158

159

d σ2/d Ω/dM 2o-8o(Lab) [μb/sr/(4MeV/ c 2)]

(α)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
2.1

2.12

2.14

2.16

2.18

2.2

2.22

MM d [GeV/c2]

Figure C.1: (α) The double diﬀerential cross section for the Λp final state mode around2.13 GeV/c2 for the forward scattering angle of θπK(Lab) = 2◦ –8◦ . This spectrum wasfitted with a Lorentzian function folded with the resolution of 1.4 MeV/c2 in σ for theΣN cusp (green line), and a Gaussian function for the ΣN → Λp conversion (blue line).
The total fitting function is also shown in the red line. (a, b, c) are the missing mass
spectra by requiring the multiplicity 1, 2 and 3, respectively, of the past experiment takenfrom Ref. [109]. The multiplicity 1 and 3 spectra correspond to the our inclusive and Λp
final state spectra, respectively. In this reference, the narrow peak around 2.13 GeV/c2
shown in dotted-line was interpreted as a resonance, which is understood as the ΣNcusp nowadays, a broad peak around 2.15 GeV/c2 indicated in dashed-line was taken
into account as the component of ΣN → Λp conversion.

Appendix D
Two-proton coincidence analysis
using the EX spectrum
In order to check the validity of this final state determination method of the two-proton
coincidence analysis, we fitted not only missing-mass squared MX2 but also missing energy
EX spectra of the d(π + , K + pp)X reaction. In this appendix, we show the two-proton
coincidence analysis result by using the EX spectrum in the d(π + , K + pp)X reaction to
identify the final state for the systematic study. Figure D.1 shows the missing energy
spectrum of EX for each M Md region. The obtained data is indicated in black points
with error bars, whose points are after subtraction of the π ± contamination fraction. The
template fits results for the Λp, Σ0 p and Y πp modes are also shown in the figure withcolored dashed-lines. These templates were constructed by the simulation with the same
assumption of Figure 5.21. As shown in Figure D.1, the separations of the templates
between Λp and Σ0 p modes seems to be worse than the case of MX2 spectra (Figure 5.21).
Thus, the result estimated from the MX2 is used for the main analysis.
From this EX template fit, we also evaluated the double diﬀerential cross section
using the same analysis scheme described in Sec. 5.2.5. The double diﬀerential crosssections for the Λp and Σ0 p modes estimated from the fit of EX spectrum are shownin Figure D.2 (a) and (b) respectively. In the systematic error evaluation, we took into
account the ambiguity for the final state determination method.

160

161
2.10 < MM d < 2.14 [GeV/ c 2 ]2.14 < MM d < 2.18 [GeV/ c 2 ]2.18 < MM d < 2.22 [GeV/ c 2 ]

60

40
100

35

50

30

80

30

CountsCountsCounts

40
60

20

40

10

20

25
20
15
10

0

0

100 120 140 160 180 200 220240 260 280
E X [MeV]

2.22 < MM d < 2.26 [GeV/ c 2 ]

5
50

100

150

200

250

0

300
E X [MeV]50

2.26 < MM d < 2.30 [GeV/ c 2 ]

12

16

10

14

100

150

200

250

300 350
E X [MeV]

2.30 < MM d < 2.34 [GeV/ c 2 ]
12
10

12

6

10

CountsCountsCounts

8

8
6

4

8
6
4

4
2

2

2

0
100 150 200

0100 150 200 250 300 350 400 450
E X [MeV]

250 300 350 400
E X [MeV]

2.34 < MM d < 2.38 [GeV/ c 2 ]0
100 150 200 250 300 350 400 450 500
E X [MeV]

2.38 < MM d < 2.42 [GeV/ c 2 ]2.42 < MM d < 2.46 [GeV/ c 2 ]

16
10

9

14

8

12

6

7

10

CountsCounts

8Counts

10

8
6

4

0
100

4
2

2

0
100 150 200 250 300 350 400 450 500 550
E X [MeV]

5
3

4
2

6

1
200

300

400

500

600
E X [MeV]

0
100

200

300

400

500

600 700
E X [MeV]

2.46 < MM d < 2.50 [GeV/ c 2 ]

data
5

Total

Counts43+π+d → K W, W → Λ p

2π+d → K+W, W → Σ0p

1
0100 200 300+

400 500

600 700 800
E X [MeV]

π+d → K W, W → Yπp

Figure D.1: Energy spectra of X obtained from the two proton coincidence events in thereaction of the d(π + , K + pp)X. Each spectrum shows the energy of X for the diﬀerent
M Md region shown in the figure. The spectra were fitted with three components ofΛp (red dashed-line), Σ0 p (magenta dashed-line) and Y πp (green dashed-line) modes
same as Figure 5.21. This fitting was carried out to check the systematic ambiguity ofthis final-state determination method.

162APPENDIX D. TWO-PROTON COINCIDENCE ANALYSIS USING THE EX SPECTRUM(a): Σp moded σ /d Ω/dM 2o-14o(Lab) [µb/sr/(15MeV/c 2)]

4
3.5
3
2.5
2
1.5
1
0.5
0
2

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

2

2

d σ /d Ω/dM 2o-14o(Lab) [µb/sr/(15MeV/c 2)](a): Λp mode
4.5

2.1

2.2

2.3

2.4
2.5
2.6
MMd [GeV/c 2]

0
2

2.1

2.2

2.3

2.4
2.5
2.6
MMd [GeV/c 2]

Figure D.2: The double diﬀerential cross section for the Λp (a) and Σ0 p (b) final statemodes estimated from the fitting of EX as shown in Figure D.1. These spectra are
obtained from the two protons coincidence events.

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