Doctoral Thesis
Search for 6ΛH hypernucleus by the (π −, K +) reaction
at J-PARC
Hitoshi Sugimura

A dissertation submitted in partial fulfillment of
the requirements for the degree ofDoctor of Science
Department of Physics
Faculty of Science
Kyoto University
January, 2014

Abstract
A hypernucleus is a characteristic bound system of an ordinary nucleus and a few hyperon, such as Λ, Σ, Ξ. A Λ-hypernucleus consists of nucleons and one Λ hyperon. Whena Λ hyperon is embedded into a nucleus, there are several interesting features theoretically expected for some specific neutron-rich hypernuclei. One example is the glue-likerole of a Λ hyperon in the hypernuclei. The glue-like role gives a critical contribution to
the binding especially around the proton- and neutron-drip lines, and may extend theboundary of nuclear stabilities. Another example is an effect of the ΛN-ΣN mixing. A
non-zero isospin of the core nucleus is essential for the large mixing because the core nucleus is a buffer of the isospin to compensate the isospin difference between Λ(I=0) andΣ(I=1). Therefore, the studies on the neutron-rich Λ hypernuclei with a large isospin
are important to understand the properties of the ΛN-ΣN mixing effect. To study its
effects, we selected a 6Λ H hypernucleus which has one proton, four-neutron, and one Λ
hyperon.
The present experiment was proposed aiming at a precise spectroscopic investigationof light neutron-rich Λ hypernuclei, 6Λ H by the (π − , K + ) reaction at 1.2 GeV/c by using
the SKS spectrometer (J-PARC E10). The FINUDA group reported the binding energyof 6Λ H based on three candidate events. We would like to much improve the precision of
the binding energy and establish the existence in high statistics. By observing more than
100 events, not only the precise binding energy but also the production cross section canbe obtained in a good statistical accuracy. It would be important in order to discuss the
ΛN-ΣN mixing effect quantitatively. The structure of the 6Λ H will be revealed for the
first time.
The 6Λ H production data by the 6 Li(π − , K + ) reaction were taken for the first time in
the K1.8 beam line of J-PARC Hadron Experimental Facility in two cycles in December
2012 and in January 2013. A 6 Li target 3.5 g/cm2 in thickness was used. The total
number of pions irradiated on the 6 Li target was 2.1×1012 .
In the missing-mass spectrum of 6 Li(π − , K + ) reaction, no peak structure was observed. We estimated an upper limit of production cross section from the number of
events with the missing-mass window. There were 3 events around the 4Λ H+2n threshold(5801.7 MeV/c2 ) We employed the upper limit of 6.68 events at 90% confidence levelfrom the Poisson statistics, and the upper limit of production cross section was estimatedto be 1.2 nb/sr at 90% confidence level.

Contents
1 Introduction
1.1 Neutron-rich Λ-hypernuclei . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Experimental approaches for the neutron-rich Λ-hypernuclei . . . . . . .
−1.2.1 The (Kstopped, π + ) reaction . . . . . . . . . . . . . . . . . . . . . .
1.2.2 (π − , K + ) reaction . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 J-PARC E10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Theoretical approach for the 6Λ H hypernucleus . . . . . . . . . . . . . . .

1
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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 . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Particle ID counters . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Tracking devices . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Scattered-particle spectrometer (SKS) . . . . . . . . . . . . . . . . . . .
2.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Data-acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Lithium-6 target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Data Analysis
3.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Analysis of beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Identification of triggered beam particles . . . . . . . . . . . . . .
3.2.2 BFT analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 BC3 and BC4 local tracking . . . . . . . . . . . . . . . . . . . . .
3.2.4 Beam momentum reconstruction . . . . . . . . . . . . . . . . . .
3.3 Analysis of scattered particles . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Hodoscope cut . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 SFT and SDC2 local tracking . . . . . . . . . . . . . . . . . . . .
3.3.3 SDC3 and SDC4 local tracking . . . . . . . . . . . . . . . . . . .
3.3.4 Momentum reconstruction of a scattered particles . . . . . . . . .
3.3.5 Particle identification in the SKS spectrometer . . . . . . . . . . .
3.4 Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2

3.5
3.6

Analysis of the beam-through runs . . . . . . . . . . . . . . . . . . . . .
Momentum correction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Momentum correction of scattered particles . . . . . . . . . . . .
3.6.3 Target energy loss and straggling . . . . . . . . . . . . . . . . . .
3.6.4 Momentum correction of beam pions . . . . . . . . . . . . . . . .

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4 Experimental results
4.1 Good (π − , K + ) events . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Acceptance of SKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Missing-mass spectrum of the 6 Li(π − , K + ) reaction . . . . . . . . . . . .

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5 Discussions
5.1 Analysis of 12Λ C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Analysis of the Σ± . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Background level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Estimation of upper limit . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Structure of 6Λ H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Conclusion

93

A Missing-mass spectrum of the 6 Li(π − , K + ) reaction

96

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9

Λ hypernuclear chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
All the hypernuclear γ transitions observed and identified to date . . . .
Nuclear chart produced each reaction . . . . . . . . . . . . . . . . . . . .
−Measurement of (Kstopped, π + ) reaction at KEK. . . . . . . . . . . . . . .
Evidence of 3 event of 6Λ H by FINUDA . . . . . . . . . . . . . . . . . . .
The missing-mass spectrum of 10 B(π − , K + ) reaction . . . . . . . . . . . .
Calculated inclusive excitation spectra . . . . . . . . . . . . . . . . . . .
Theoretical calculation of 6Λ H binding energy. . . . . . . . . . . . . . . . .
5
H spectrum measured in coincidence with triton from the decay of theresidual 5 H system [42]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.10 Missing-mass spectra for the 9 Be(π − , pt)X reaction . . . . . . . . . . . .
1.11 Missing-mass spectra for the 9 Be(π − , dd)X reaction . . . . . . . . . . . .
2.1 A schematic view of J-PARC Facility . . . . . . . . . . . . . . . . . . . .
2.2 The schematic view of hadron experimental facility as of 2013. . . . . . .
2.3 Schematic view of K1.8 beam line . . . . . . . . . . . . . . . . . . . . . .
2.4 Typical beam profile at the target . . . . . . . . . . . . . . . . . . . . . .
2.5 Schematic view of K1.8 beam spectrometer. . . . . . . . . . . . . . . . .
2.6 The schematic view of GC. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 A schematic view of BH2. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 The structure of BFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 The cell structure of BC3·4 . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 The picture of SSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Beam rate dependence of the SSD performances . . . . . . . . . . . . . .
2.12 A schematic view of the SKS . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 A schematic view of TOF. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14 Threshold and refractive index for Čerenkov radiation as a function of the
momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.15 A schematic view of LAC. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 A schematic view of LC. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.17 Schematic view of SFT. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 The cell structure of SDC3·4 . . . . . . . . . . . . . . . . . . . . . . . . .
2.19 PIK trigger logic diagram. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.20 The selected TOF and LC segments region with the matrix trigger . . . .
2.21 Logic Scheme of the mass trigger . . . . . . . . . . . . . . . . . . . . . .
2.22 Diagram of the data-acquisition system. . . . . . . . . . . . . . . . . . .
4

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LIST OF FIGURES

5

2.23 The Picture of 6 Li target . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3.1
3.2
3.3
3.4
3.5

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Typical BH2 time spectrum of the incident beam particles . . . . . . . .
Slewing correction of BFT . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical TDC distribution of BFT . . . . . . . . . . . . . . . . . . . . . .
Typical TDC distribution of one of BC3·4 layers . . . . . . . . . . . . . .
A scatter plot between the drift time and the drift length of one of theBC3·4 layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Local position coordinate for the local straight tracking. . . . . . . . . . .
3.7 The VI and VO point in the K1.8 beam line spectrometer . . . . . . . .
3.8 (a) Typical residual distribution of one of the BC3·4 layers. (b) Typicalχ2 distribution of the BC3·4 tracking. . . . . . . . . . . . . . . . . . . . .
3.9 Typical distribution of the beam momentum at 1.2 GeV/c . . . . . . . .
3.10 Typical distribution of XY and UV . . . . . . . . . . . . . . . . . . . . .
3.11 Typical residual and χ2 distributions of SFT·SDC2 local tracking. . . . .
3.12 Typical residual distribution of one of the SDC3·4 planes (left), and χ2
distribution of SDC3·4 (right). . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Typical χ2 distribution of SKS tracking. . . . . . . . . . . . . . . . . . .
3.14 Scattered particle mass squared distribution for the 6 Li(π − , K + ) data . .
3.15 The correlation of the mass squared and the momentum. . . . . . . . . .
3.16 Typical distribution of the scattering angle difference . . . . . . . . . . .
3.17 Distributions of a vertex and a closest distance. . . . . . . . . . . . . . .
3.18 The momentum difference between the two spectrometers. . . . . . . . .
3.19 The width of momentum difference . . . . . . . . . . . . . . . . . . . . .
3.20 dx/dz and dy/dz correction for scattered particles . . . . . . . . . . . . .
3.21 Distributions of the momentum difference between the two spectrometerswith and without target . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.22 Momentum difference measured with the K1.8 beam line and the SKS.
Fulled circles represent beam through runs at beam momenta of 0.8, 0.9,
1.0 and 1.2 GeV/c. Open circle represents momentum difference of theΣ+ production run, where expected beam momentum is estimated withthe mass difference from PDG value of Σ+ . . . . . . . . . . . . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

Flow chart of the offline analysis . . . . . . . . . . . . . . . . . . . . . . .
Time distribution of LAC in proton event in the (π, K) trigger. . . . . .
The correlation of time-of-flight and scattering angle (dx/dz). . . . . . .
The SKS tracking efficiency as a function of the scattering angle. . . . . .
The missing-mass resolution of Σ− as a function of the χ2sks . . . . . . . .
The number of PIK tracks candidates. . . . . . . . . . . . . . . . . . . .
Vertex reconstruction efficiency as a function of the scattering angle. . . .
Scatter plot between the scattering angle and z-vertex distribution for the(π − , K + ) data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 The acceptance of SKS in the 2.2 T mode. . . . . . . . . . . . . . . . . .
4.10 The integrated acceptance of SKS in the 2.2 T mode. . . . . . . . . . . .
4.11 Missing-mass spectrum of the 6 Li(π − , K + ) reaction . . . . . . . . . . . .

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5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8

Excitation energy spectrum of the 12 C(π + , K + )12
Λ C reaction . . . . . . . .
Missing-mass spectrum of Σ± . . . . . . . . . . . . . . . . . . . . . . . . .
The differential cross section of the Σ− production . . . . . . . . . . . . .
The differential cross section of Σ+ production . . . . . . . . . . . . . . .
The differential cross section of the Σ− production compared with oldexperiment as a function of the beam momentum . . . . . . . . . . . . .
The differential cross section of Σ+ production compared with old experiment as a function of the beam momentum . . . . . . . . . . . . . . . .
Background level in the over bound regions of the 6 Li(π − , K + ) reaction .
Level sturucture of 6Λ H with respect to the particle decay threshold of4
Λ H+2n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Tables
2.1
2.2
2.3
2.4
2.5
2.6
2.7

Design specifications of the K1.8 beam line spectrometer . . . . . . . . . 19
Specifications of the particle identification counters in the beam line spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Specifications of the tracking devices in the beam line spectrometer. . . . 23
Design specifications of the new SKS spectrometer at 2.16 T mode. . . . 27
Specifications of the particle identification counters in the SKS spectrometer 29
Specifications of the tracking devices in the SKS spectrometer. . . . . . . 32
Summary of runs. Target material and thickness, and beam momentum
and intensity are listed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.1
3.2
3.3
3.4

The position resolution of each layers. . . . . . . . . . . . . . . . . . . . .
Slit condition of 6 Li(π − , K + ) production reaction . . . . . . . . . . . . .
target energy loss and stragglings . . . . . . . . . . . . . . . . . . . . . .
momentum correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46
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4.1
4.2

The list of the experimental efficiency factors. . . . . . . . . . . . . . . .
Typical materials in the spectrometers along the flight path. . . . . . . .

6878

A.1 The missing-mass spectrum of the 6 Li(π − , K + ) reaction as a table . . . .

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Chapter 1
Introduction
1.1

Neutron-rich Λ-hypernuclei

A hypernucleus is a characteristic bound system of a few hyperons, such as Λ, Σ, Ξ andan ordinary nucleus. A Λ-hypernucleus consists of one Λ hyperon and nucleons.
Hypernuclear investigations provide invaluable information on hadronic many-bodysystems by introducing a new degree of freedom “strangeness” [1, 2, 3]. New structuresof baryonic many-body systems can be better studied with spectroscopic measurements.
In particular, a Λ hyperon can be put deep inside a nucleus as an impurity and provides
a sensitive probe of the nuclear interior. Since the Λ hyperon does not suffer from Pauliblocking with other nucleons, it can penetrate into the nuclear interior and form deeplybound hypernuclear states. It is expected that new forms of hadronic many-body systems
can be investigated using this new degree of freedom, strangeness, and hypernucleus isalso a good tool to investigate the two-body Λ-N interaction.
Since the first discovery of a cosmic-ray induced hyperfragment production event inemulsion [4], various Λ-hypernuclei have been observed. The binding energies of light(A < 16) Λ hypernuclei were measured from their weak decays in emulsion, and theΛ potential depth was found to be ∼2/3 that of the nucleon. However, at that time,the experimental data was limited to the binding energies of ground states, and excitedstates were not able to be investigated.
In 1970s and 1980s, extensive studies have been made with counter experiments byusing K − beams at the European Organization for Nuclear Research (CERN) and later at
Brookhaven National Laboratory (BNL) [5, 6, 7]. Spectroscopic studies including excitedstates of hypernuclei had become possible with the in-flight (K − , π − ) reaction. A noble
method of the in-flight (K − , π − ) reaction in an almost recoilless condition was introduced
16
and hypernuclei such as 9Λ Be, 12
Λ C and Λ O were intensively studied [8, 9, 10, 11].
++
The use of (π , K ) reaction began at the Alternating Gradient Synchrotron(AGS) of
BNL and High Energy Accelerator Research Organizaion(KEK)-Proton Synchrotron [12,13, 14, 15]. The (π + , K + ) reaction selectively populates angular momentum stretchedstates because of a large momentum transfer of ∼350 MeV/c to a recoil hypernucleus.
This is in contrast to the (K − , π − ) reaction, which transfers a small momentum to a
hypernucleus and therefore favors the excitation of substitutional states. By using thisreaction, high-quality excitation energy spectra were measured for various Λ hypernuclei
1

2

CHAPTER 1. INTRODUCTION

and hypernuclear spectroscopy was established as a broadly applicable, quantitative tool
up to 208
Λ Pb.

Figure 1.1: Λ hypernuclear chart. The experimentally identified Λ hypernuclei andthe experimental methods used to study them (reaction spectroscopies of (K − , π − ),(π + , K + ), (e, e′ K + ), etc., γ spectroscopy, and the emulsion method) are shown.
In light Λ hypernuclei, the spin-dependent parts of the Λ-N interaction such as spinspin, spin-orbit, and tensor interactions have important roles on fine level structures. A
high energy resolution of less than a few 100 keV is required to measure the splitting
because the spin-dependent Λ-N interactions are known to be very small. Precision
spectroscopy has been carried out with unprecedented resolution of a few keV through theuse of a germanium detector array called Hyperball [16]. It has provided new quantitative
information on spin-spin, spin-orbit and tensor interactions of the Λ-N interaction byobserving the fine structures as shown in Fig 1.2. Although, we have a long history ofΛ-hypernuclei, the observed Λ hypernuclear species are limited as shown in Fig. 1.1.
On the other hand, as for the Σ hypernuclei, the observation of 4Σ He bound state by
the in-flight (K − , π − ) reaction at BNL [17] was one of the great success confirming of any
bound sate of hypernuclei containing Σ hyperon which was first claimed in KEK using−(Kstopped, π ± ) reaction [18]. Existence of this bound state in 4 He was first predictedin theory by Harada et al. in 1990 [19]. According to their theory, a strong isospindependence of the ΣN interaction plays an important role in populating the the rather
narrow bound state. And no other bound states in medium to heavy Σ hypernuclei are
expected after a measurement of 28 Si(π − , K + ) reaction suggesting a strong repulsion of
about 30 MeV [20].
Interesting property connecting Λ and Σ hypernuclei is the effect of the ”ΛN-ΣN
mixing”. The ΛN-ΣN mixing was first discussed by Gibson et al. for s-shell Λ hypernuclei [21]. Since the mass difference of Λ and Σ, MΣ -MΛ ∼80 MeV/c2 is narrower
than that of ordinary nuclei, M∆ -MN ∼290 MeV/c2 , this situation makes the effect1.1. NEUTRON-RICH Λ-HYPERNUCLEI

3

Figure 1.2: All the hypernuclear γ transitions observed and identified to date for
4
4
7
9
10
11
15
16
Λ H [22],Λ He [23], Λ Li [24], Λ Be [25], Λ B [26],Λ B [27],Λ N [28], Λ O [28]. The level schemesof these hypernuclei with the energies (in MeV) and the assigned spins and parities areshown together with the reactions used to populate the excited states in γ spectroscopy
experiments.

4

CHAPTER 1. INTRODUCTIONof the ΛN-ΣN coupling strong. A non-zero isospin of the core nucleus is essential forthe large mixing because the core nucleus is a buffer of the isospin to compensate theisospin difference between Λ (I=0) and Σ (I=1). The idea has been extended to thecoherent ΛN-ΣN mixing by Akaishi et al. to understand the binding energy of s-shellΛ-hypernuclei systematically [29]. The strong ΛN-ΣN coupling introduces an additional
effective two-body attraction between Λ and nucleon.
Therefore, the studies on the neutron-rich Λ-hypernuclei with a large isospin areimportant to understand the properties of the ΛN-ΣN mixing effect. Since the ΛN-ΣN
mixing induces the three-body ΛNN interaction, the mixing effect may play an importantrole in the high-density strange matter, such as the matter in the core of the neutronstars [30]. The study of the neutron-rich Λ hypernuclei is one of approaches to understandthe details of the effect of the Λ hyperon at the boundary of stability of nuclei and theΛNN three-body interaction.
To study these effects, we selected a 6Λ H hypernucleus which has one proton, fourneutron, and one Λ hyperon. We would expect large structure change of the core nucleus
beyond the neutron drip line by the addition of a Λ hyperon. If it is bound, we would
obtain information of ΛN-ΣN mixing effect from the binding energy and production crosssection. The study of the 6Λ H hypernucleus also provide the information of the structureof 5 H.

1.2. EXPERIMENTAL APPROACHES FOR THE NEUTRON-RICH Λ-HYPERNUCLEI5

1.2

Experimental approaches for the neutron-rich Λhypernuclei

The single charge-exchange reaction (SCX), such as the (e, e′ K + ) reaction converts one
proton to one Λ hyperon (p → Λ). The double charge-exchange (DCX) reaction, suchas the (K − , π + ) and (π − , K + ) reactions, converts two protons to one Λ hyperon and one
neutron (pp → nΛ). These two reactions are promising spectroscopic tools to access theΛ-hypernuclei close to the neutron drip-line [31]. Figure 1.3(b) shows the hypernuclei
which have ever produced in the A < 16 region: purple and green colored ones wereobserved as hyperfragments in nuclear emulsion experiments. Although the chart looks
already compatible with that of the ordinary nuclei, Fig 1.3(a), a variety of Λ hypernuclei
are expected to exist due to a glue-like role of a Λ hyperon. By using the SCX or DCX
reactions, wider areas can be accessed as shown in Fig 1.3(c).

1.2.1

−
, π + ) reaction
The (Kstopped

The first study of the neutron-rich Λ-hypernuclei with the DCX reaction was performed−, π + ) reaction [32].
at the KEK 12-GeV proton synchrotron facility by using the (Kstopped−+
There are a few processes contributing to the (Kstopped , π ) spectra. One is a quasi-freeΣ− production of
K − + p → π + + Σ− ,(1.1)
which produces π + ’s with their momenta lower than 170 MeV/c. The signal of the
2p → Λn conversion process is assumed to be produced through a two-step process of
K − + p → Λ + π 0 , π 0 + p → π + + n.

(1.2)

In reaction 1.2, π + momentum region of interest is around the end point of quasi-free Λ
production (π + momentum ∼ 250 MeV/c) where the binding energy between hyperon
and core nucleus is zero. Another source of π + ’s comes from the decay of Σ+ → π + n
produced from a quasi-free production of K − p → Σ+ π − . The π + momentum range
overlaps in the signal region. Figure 1.4 shows the π + momentum spectra measured fromthree kinds of targets, 9 Be, 12 C and 16 O. Due to the in-flight decay π + background from
Σ+ → nπ + , no clear peak was observed, and upper limits of the formation probabilities−5
per stopped K − were estimated to be 2.3 × 10−4 in 9Λ He, 6.1 × 10−5 in 12
Λ Be and 6.2 × 10
in 16
Λ C, respectively.
The Fisica Nucleare a DAΦNE(FINUDA) collaboration also performed a measure−, π + ) reaction in their first data taking [33]. The clear idenment with the 6 Li(Kstopped
tification of the production of the neutron-rich hypernuclei, however, was not accomplished in the inclusive π + spectra. Recently, in the second data taking by improving
the statistics, they have succeeded to observe three candidate events of 6Λ H with thesimultaneous detection of both the production of (K − , π + )6Λ H and the mesonic decay of− 66Λ H→ π + He [34]. Figure 1.5 shows the momentum correlation between the produced
π + and decay π − from 6Λ H after a kinematical cut. The left figure shows tight kinematicalcut and right one shows the loose cut. They reported the number of events (3 event) in
the red box does not change for both figures. On the other hand, number of events in

6

CHAPTER 1. INTRODUCTION

Figure 1.3: (a) chart of light ordinary nuclei. (b) chart of Λ hypernuclei ever producedin the A < 16 region. Purple boxes correspond to directly produced hypernuclei via the(K − , π − ) and (π + , K + ) reactions on stable nuclear targets and green boxes correspondto hypernuclei observed as hyperfragments in the emulsion experiments. (c) blue boxes
show hypernuclei to be produced by the SCX reactions and yellow boxes correspond to
hypernuclei to be produce by DCX reactions on stable targets.

1.2. EXPERIMENTAL APPROACHES FOR THE NEUTRON-RICH Λ-HYPERNUCLEI7
the blue box are decreased in the tight cut. Therefore, they interpreted the 3 events are
not background but candidates of 6Λ H hypernucleus. The production rate was estimated−to be (2.9 ± 2.0) × 10−6 /Kstop. Furthermore, they reported a binding energy for 6Λ H was(4.0 ± 1.1) MeV with respect to 5 H+Λ. However, because of the small number of thecandidate events, the FINUDA observation should be confirmed with higher statistics.

−, π + ) reaction on (a) 9 Be, (b) 12 C and
Figure 1.4: π + momentum spectra in the (Kstopped
16(c) O targets [32].

8

CHAPTER 1. INTRODUCTION

Figure 1.5: π + momentum vs π − momentum for 6 Li target events. The shaded (red)rectangle on each side consists of a subset of events with pπ+ = 250–255 MeV/c and p−π=
130–137 MeV/c. The figures were taken from the literature [34].

1.2.2(π − , K + ) reaction

Another DCX reaction, the 10 B(π − , K + ) reaction at 1.05 and 1.2 GeV/c, was measured
in the KEK-E521 experiment [35].
Naive reaction mechanisms of the (π − , K + ) reaction are the ”two-step” reactions asfollows;
π − + p → K 0 + Λ, K 0 + p → K + + n,andπ − + p → π 0 + n, π 0 + p → K + + Λ.
The two-step reaction mechanisms usually predict larger cross sections at the pion
beam momentum around 1.05 GeV/c because the Λ production reactions in the twostep process have a local maximum at the beam momentum. However, they observed
the beam momentum dependence different from this expectation.
There could be another reaction mechanism of a one-step reaction mechanism asfollows,
π − + p → K + + Σ− , Σ− p → Λn.
The second step in the process is the conversion from Σ− p to Λn through the ΛN-ΣN
mixing. The one-step mechanism predicts larger cross section at higher beam momenta
because the pion beam momentum for the virtual Σ− production favors higher momenta.
KEK-E521 experiment was performed with SKS spectrometer system [36] in K6 beamline at KEK Proton Synchrotron Facility. At first, they set the beam pion momentum at
1.05 GeV/c where the cross section has the maximum if the two-step process is dominant.
However, the events in the bound region was only 7 counts, and they obtained the crosssection of 5.8 ± 2.2 nb/sr, which is much smaller than a theoretical estimation for the
ground state doublet based on the two-step mechanism.

1.2. EXPERIMENTAL APPROACHES FOR THE NEUTRON-RICH Λ-HYPERNUCLEI9
Thus, the beam momentum was raised to 1.2 GeV/c, and the number of measured
events was increased to 47 events. The production cross section was 11.3 ± 1.9 nb/sr.
Figure 1.6 shows the missing-mass spectrum of 10 B(π − , K + ) reaction. Since there wasno physical background in the (π − , K + ) reaction in the bound region, the 10Λ Li production
events were clearly observed. From this result, the production cross section of DCX isfound to be roughly 10−3 of that of the non charge-exchange (π + , K + ) reaction. Based

Figure 1.6: The missing-mass spectrum of the 10 B(π − , K + ) reaction measured in [35].
The inset shows a closeup of the Λ bound region.
on the KEK-E521 experiment, a theoretical calculation of the double charge-exchange
reaction was performed by Harada et al. [37]. Figure 1.7 shows the calculated inclusive
excitation spectrum with the one-step mechanism for the 10 B(π − , K + ) reaction at pπ =1.20 GeV/c. In the top figure, intermediate Σ nucleus potential, WΣ , is scanned whenthe mixing potential of VΛΣ is fixed at 11 MeV. In the bottom figure, VΛΣ is scanned
when WΣ is 20 MeV. As a result, when the magnitude of probability of Λ − Σ mixing is
0.57%, the theoretical spectrum is in good agreement with the experimental data.

10

CHAPTER 1. INTRODUCTION

12
11
10
8
4

40

50

30
20
10

Figure 1.7: Calculated inclusive excitation spectra with the one-step mechanism for the10
B(π − , K + ) reaction at pπ = 1.20 GeV/c, together with the experimental data [35].
(Top) The solid curves denote the K + spectra by VΣΛ =4,8,10,11,12 MeV when -WΣ =20
MeV, with a detector resolution of 2.5 MeV(FWHM). (Bottom) The solid curves denotes-WΣ =10,20,30,40,50 MeV when VΣΛ = 11 MeV (PΣ = 0.57%). The dashed curve denotes
the inclusive Λ spectrum by the two-step mechanism.

1.3. J-PARC E10

1.3

11

J-PARC E10

The present experiment was proposed aiming at a precise spectroscopic investigationof light neutron-rich Λ-hypernuclei, 6Λ H via the (π − , K + ) reaction by using the SKS
spectrometer.
The same π − momentum of 1.2 GeV/c was selected as in the KEK-E521 experiment.
The FINUDA group reported the binding energy of 6Λ H based on three candidate events.
We would like to much improve the precision of the binding energy and establish theexistence in high statistics. A high-intensity π − beam at J-PARC and a large acceptanceof the SKS spectrometer have good merits for this purpose. We also introduced high-rate
tracking detectors such as scintillating fiber detectors and silicon strip detectors for theE10 experiment. By observing more than 100 events, not only the precise binding energy
but also the production cross section can be obtained in a good statistical accuracy. It
would be important in order to discuss the ΛN-ΣN mixing effect, quantitatively. The
structure of the 6Λ H will be revealed for the first time.

1.4

Theoretical approach for the 6ΛH hypernucleus

Theoretical calculations on 6Λ H have been performed with various models and interactions. We have summarized the binding energy of the 6Λ H ground state of theoretical
calculations compared with FINUDA data in Fig. 1.8. The ground state of 5 H is theresonance of 1.7 MeV with respect to 3 H+2n, and 4Λ H hypernucleus is bound by 2.0 MeV
with respect to 3 H+Λ.
A highly neutron-rich Λ-hypernucleus 6Λ H was first discussed by Dalitz and LeviSetti [38]. They predicted the Λ binding energy of the ground state to be 4.2 MeV byusing central part of ΛN interaction. Akaishi et al suggested a considerably large binding
energy of 5.8 MeV for the 0+ ground state of 6Λ H due to a rather large contributionof 1.4 MeV from the coherent ΛN-ΣN coupling [39]. The coherent ΛN-ΣN coupling
was considered to solve over binding problem of s-shell hypernuclei such as 3Λ H, 4Λ H,
5
4
Λ He and Λ He [29]. Gal and Millener estimated it by a phenomenological shell-model
calculation [40], and obtained the binding energy of 3.83 ± 0.08 ± 0.22 MeV. Hiyama
et al. performed the four-body cluster-model calculation with t(triton) + n + n + Λ,and obtained the binding energy of 2.57 MeV [41]. This calculation is the only one
that considers dynamically the 5 H core as a three-body 3 H−n − n resonance, and it
disregards the Λ − Σ coupling effect. These theoretically calculated binding energies
were distributed as shown in Fig. 1.8 from bound to unbound regions with respect to the4Λ H+2n decay threshold, which corresponded to the Λ binding energy of 3.7 MeV. They
were quite sensitive to the ΛN interaction and the properties of the core nucleus 5 H.

12CHAPTER 1. INTRODUCTION

5

H+Λ

0 MeV

H + 2n + Λ

1.7 MeV

Hiyama2.57 MeV4
H + 2nΛ

3.7 MeV

Gal, Millener

3.83 MeV
4.2 MeV3

Dalitz

1.4 MeV
Akaishicoherent
Λ-Σ coupling

4.0 MeV6
H (FINUDA exp)
Λ

5.8 MeVFigure 1.8: Theoretical calculation of 6Λ H binding energy.
5

H, the core nucleus of 6Λ H, was first produced at Joint Institute for Nuclear Research(JINR). They measured two protons emitted from the decay of 2 He with the reaction of p(6 He,2 He) [42], and found the 5 H is the resonance state of 1.7 ± 0.3 MeV
with respect to t + n + n threshold with a width of 1.9 ± 0.4 MeV. Figure 1.9 shows
the missing-mass spectrum of the p(6 He,2 He) reaction. Extensive studies have been
made at Helmholzzentrum fur Schwerionenforschung GmbH (GSI) and Los Alamos Meson Physics Facility(LAMPF) [43, 44] by using 9 Be(π − , pt) and 9 Be(π − , dd) reactions asshown in Fig 1.10 and Fig 1.11. No clear peak structure was observed in both experiments not only bound states but also resonance states. Therefore, the existence of the5
H state is not established yet. A precise study will be conducted at RCNP in the near
future.
The present thesis consists of six chapters and one appendix. Chapter 2 describes
the experimental apparatus. As mention above, to accumulate large number of event,
it is necessary to use high intensity beam. In preparing of the present experiment, wehave developed some new detectors and electronics for high rate operation. Chapter 3
describes the data analysis. After data taking, I analyzed all the data, in which special
cares were taken to reduce the background event around the bound region. Since theproduction cross section of (π − , K + ) reaction is a few nb/sr level, it is important to reducethe background event as much as possible. Also, in that chapter, elaborate calibration
procedures of the momentum is described. Chapter4 describes the experimental results,
Chapter 5 the physics discussions about the results, and Chapter 6 a conclusion.

1.4. THEORETICAL APPROACH FOR THE 6Λ H HYPERNUCLEUS

13

Figure 1.9: 5 H spectrum measured in coincidence with triton from the decay of theresidual 5 H system [42].

Figure 1.10: Missing-mass spectra for the 9 Be(π − , pt)X reaction without (a) and with(b) restriction on the momentum of residual nuclei. The solid lines are the fit andBreit-Wigner distributions. Curve 1 is the sum of phase space distributions for all open
channels, curve 2 is the phase space distribution for the break up of 9 Be into p+t+4 H+n,
curve 3: p + t + t + n + n; curve4: p + t + d + n + n + n.

14

CHAPTER 1. INTRODUCTION

Figure 1.11: Missing-mass spectra for the 9 Be(π − , dd)X reaction without (a) and with(b) restriction on the momentum of residual nuclei. The solid lines are the fit andBreit-Wigner distributions. Curve 1 is the sum of phase space distributions for all open
channels, curve 2 is the phase space distribution for the breakup of 9 Be into d+d+4 H+n;
curve 3: d + d + t + n + nChapter 2
Experiment
2.1

Outline

The present experiment was carried out from December 2012 to January 2013 as J-PARC
E10 in the K1.8 beam line of J-PARC Hadron Experimental Facility. The purposeof the experiment is to produce the neutron-rich Λ-hypernucleus 6Λ H by the (π − , K + )reaction with good energy resolution and high statistics, and to study its structure andestablish the existence of 6Λ H. To obtain the high energy resolution, we used the K1.8
beam line spectrometer and superconducting kaon spectrometer (SKS). In Chap.2.2, The
accelerator of J-PARC and Hadron Experimental Facility are described. In Chap.2.3,
The detail of K1.8 beam line is described. The details of the K1.8 beam line and the
SKS spectrometers are described in Chap. 2.4 and Chap. 2.5, respectively.

2.2

J-PARC and Hadron experimental facility

J-PARC (Japan Proton Accelerator Research Complex) (Fig. 2.1) [45] is a high intensity
proton accelerator facility which aims to pursue frontier in nuclear physics, particle
physics, materials and life science and nuclear technology, using a new proton accelerator
complex with the highest beam power in the world.
H− is produced at an ion source and accelerated by Linac upto 400 MeV (50 mA) [46].
The accelerated H− is converted to a proton (H+ ) and injected to the 3 GeV RapidCycling Synchrotron (RCS) which accelerates protons to 3 GeV (333 µA) [47]. Finally,
part of protons are injected to Main Ring (MR) and accelerated up to 50 GeV (15µA) [48]. The 50-GeV proton beams are provided to the hadron facility and the secondary
hadron beams are produced for experiments. In 2010, the beam energy after Linac was
189 MeV. In the phase-1 of the J-PARC construction, the beam energy is 30 GeV and thegoal of the beam intensity is 9 µA (270 kW). The operation of the J-PARC accelerator
was started in 2009.
The primary proton beam from the main ring was extracted for a duration of 2.0
seconds in every 6.0 seconds, which is synchronized to the J-PARC 30-GeV PS operation
cycle. This duration of the beam extraction is called a spill.
The J-PARC E10 experiment was performed at the K1.8 beam line in the hadronexperimental facility (Fig. 2.2). The facility consists of a primary beam line, several
15

16

CHAPTER 2. EXPERIMENT

Hadron experimental facility
3 GeV synchrotron (RCS)
Accelerator-Driven
Transmutation System
Experimental Facility

50 GeV synchrotron (MR)

Linac

Material & Life
Science Facility

Neutrino Facility

Figure 2.1: A schematic view of J-PARC Facility.

secondary beam lines where individual experiments are set up. The proton beam istransported from the Main Ring to the hadron facility and bombarded to the production
target, T1. In the present experiment, the production target was a gold rod (6 × 6 × 60mm). The hadronic beams (kaons, pions, and so on) produced at T1 are delivered toan experimental area through secondary beam lines. Thus, the secondary beams areavailable for several lines (K1.8BR, K1.1BR and KL) simultaneously.

Hadron Experimental Facility
Beam line

K 1.8BRK 1.8

T1 targetBeam
fr om MR

KL

Beam
Dum p

K 1.1BR
56m
Figure 2.2: The schematic view of hadron experimental facility as of 2013.

2.3. K1.8 BEAM LINE

17

Figure 2.3: Schematic view of K1.8 beam line

2.3

K1.8 beam line

The K1.8 beam line is a general-purpose mass-separated beam line that can supply
various secondary hadron beams up to 2.0 GeV/c [49]. The most important designprinciple is to supply both high-intensity and high-purity kaon beams for an investigationof the S = −2 hypernuclei. The K1.8 beam line is designed to archive the K − /π − ratioof larger than 1 providing the kaon beam intensity of 10 MHz on an experimental target.
Figure 2.3 shows a schematic view of the K1.8 beam line. The beam line consists of four dipole magnets(D1–D4), thirteen quadruple magnets(Q1–Q13), four sextuple magnets(S1–S4), two electrostatic separators(DC separator) with four correction
magnets(CM1–CM4) and four slits(IF, MOM, MS1, MS2). The total length of the beamline is about 46 m.
The secondary pions were produced by the primary proton beam in a production
target located at the most upstream of the K1.8 beam line as shown in Fig.2.2. In thepresent experiment, a gold rod of 6 mm×66 mm was used as a production target. The
primary beam intensity on the production target was typically 1.4 × 1013 /spill (10kW
operation) in December 2012 and 1.8 × 1013 /spill (15kW operation) in January 2013,
respectively. The pion beam was selected by the DC separaters. The maximum gradientof the electro static field is 750 kV/cm between the 10 cm gap. In the present experiment,
both the DC separaters were set to 150 kV/cm.
After the momentum and mass selections, the pion beam was achromatically focusedon the experimental target. In the present experiment, the central beam momentum
was set at 1.2 GeV/c for the 6 Li(π − , K + ) reaction. A typical momentum bite was about

CHAPTER 2. EXPERIMENT
3500
3000

CountsCounts

18

(a)

7000
6000

2500

5000

2000

4000

1500

3000

1000

2000

500

1000

0
-50 -40 -30 -20 -10 0 10 20 30
Horizontal position (X) [mm]

40

50

(b)

0
-50 -40 -30 -20 -10 0 10 20 30
Vertical position (Y) [mm]4050Figure 2.4: Typical beam profile at the experimental target in the E10 experimentmeasured by tracking chambers at the downstream of the K1.8 beam line spectrometer.
The horizontal (a) and vertical (b) positions are shown.
2% (FWHM) determined by the setting of the momentum slit (MOM). The measured
beam size at the experimental target position by tracking chambers at the downstreamof the K1.8 beam line spectrometer was typically 56W ×28H (mm2 ) in FWTM, as shownin Figure 2.4.

2.4

K1.8 beam line spectrometer

The end-part of the K1.8 beam line is used as a beam spectrometer [50] to analyze
momentum and trajectory of each beam particle. Figure 2.5 shows the schematic viewof the K1.8 beam line spectrometer. The beam spectrometer consists of a gas Čerenkov
counter (GC), a scintillating fiber tracker (BFT), QQDQQ magnets, two drift chambers(BC3 and BC4) and a timing plastic scintillation hodoscope (BH2).
Beam trajectories are measured by BFT and BC3-BC4 for momentum analysis andreaction vertex reconstruction. For the momentum reconstruction, a third-order transfer matrix was used through the QQDQQ system. In order to minimize the multiple
scattering effect on the momentum resolution, the hx|θi term of the transport matrix
was tuned to be zero. The design momentum resolution is 3.3 × 10−4 (FWHM) with theposition accuracy of 0.2 mm (rms). The magnetic field of the dipole magnet (D4) wasmonitored during the experiment with a high-precision Hall Probe [Digital Tesla meter
151 (DTM-151)] with the accuracy of 1.7 × 10−6 [51]. The observed fluctuation was lessthan 0.05% during the data taking period. Design specifications of the K1.8 beam line
spectrometer are listed in Table 2.1.

2.4. K1.8 BEAM LINE SPECTROMETER

19

K1.8 beam line spectrometer5m

target
BH2
BC4
BC3

Q13

Q12
D4
BFT
GC

Q10 Q11
Figure 2.5: Schematic view of K1.8 beam spectrometer.

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 m
4m

20

2.4.1

CHAPTER 2. EXPERIMENT

Particle ID counters

Particle ID couters of K1.8 beam line spectrometer were comprised of GC and BH2.
Specifications of the particle ID counters are listed in Table 2.2. GC and BH2 are
installed for identifying incoming pion beam.
Table 2.2: Specifications of the particle identification counters in the beam line spectrometer
Name Sensitive area
Spec.
PMT
W×H×T (mm)(Hamamatsu)
L
GC 340×80(mirror), 290
iso-C4 H10 , n∼1.002 (1.5 atm) R1250-03 (UV glass)BH2 118×60×5
8 segments, 3-stage booster
E10679GC
The Čerenkov counter, GC, is installed at the most upstream of the K1.8 beam line
spectrometer in order to reject electrons. Figure 2.6 shows a schematic view of GC. The
pressured isobutane-gas (0.15 MPa) was used. In addition, to increase the detection
efficiency, the 5” PMT with a UV transparent window was equipped. A reflection mirror was made of a borosilicate glass coated with aluminum. In order to resist against
oxidation, the surface of the alminium was coated with the manganese fluoride (MgF2 )which is transmissive in the ultraviolet-light region. The configuration of the mirror and
the PMT was optimized to focus the Čerenkov radiation on to the photo-cathode of the
PMT. The number of photo-electrons detected by GC was about 5 for electrons with themomentum of larger than 0.5 GeV/c.

2.4. K1.8 BEAM LINE SPECTROMETER

21

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 2.6: The schematic view of GC.

22

CHAPTER 2. EXPERIMENT

BH2
BH2 is a segmented plastic scintillation counter located 120 cm upstream of the experimental target to define the time zero for all the timing measurements. Figure 2.7 showsa schematic view of BH2. It was segmented into 8 vertical pieces of 5-mm thick plastic
scintillators. The horizontal size of each segment is adjusted for the single counting rateof each segment to be uniform considering the beam profile. 3”/8 phototubes with athree-stage booster were connected on both ends of each segment.
Y

Acrylic
Light Guide

Beam

Scintillater
BC420
X
60mm

118mm
7mm
t = 5mm
7mm

10mm 35mm

Figure 2.7: A schematic view of BH2.

2.4. K1.8 BEAM LINE SPECTROMETER

2.4.2

23

Tracking devices

Specifications of the tracking devices in the beam line spectrometer are summarized inTable 2.3.
Table 2.3: Specifications of the tracking devices in the beam line spectrometer.
Name
BFT
BC3
BC4
SSD

Effective area
W×H (mm)
160×80
192×150
192×150
61×61

pitch
(mm)
1.0
1.5
1.5
0.08

Wires
xx′
xx uu′ vv ′vv ′ uu′ xx′xy′

Angle (x, u, v)(◦ )00, +15, −150, +15, −150, +90

Typical resolution(µm in r.m.s)
200
200
200
20

BFT
At the entrance of the K1.8 beam line spectrometer, particle trackers should be operated
under a very high counting rate at 10–20 MHz. To improve the high-rate tolerance andmeasure the time information precisely, a scintillating fiber tracker (BFT) was installed
just upstream of Q10 magnet. The high-rate tolerance was checked by using proton beamat 400 MeV in RCNP [52]. The efficiency was kept more than 95% at 1 MHz/fiber. BFT
is a scintillating fiber tracker with a xx′ structure and is made of scintillating fibers
with 1 mm diameter. The light signals from the scintillating fibers are read out by
Multi Pixel Photon Counters(MPPCs). The Extended Analogue SiPM ReadOut Chip
(EASIROC) system was used [53] as read out electronics. The EASIROC was developed
at Linac Accelerator Laboratory (LAL) in France. EASIROC has 32 MPPC inputs andall essential functions to operate many MPPCs such as amplifier, discriminator and bias
adjustment for MPPCs. The multi-hit tdc program has developed by rewriting the FPGAin EASIROC chip. The encoded data is transferred through the SiTCP connection.

24

CHAPTER 2. EXPERIMENTMPPC circuit board

Position pin

MPPC (S10362-100P)

Fiber end point
25.09

Position pin

72-M2x0.4 深さ8

25.89

3.96

Fiber end point
160- 1 貫通

80

506

19.4

5.05

4.4

11.9

13.7

4.4

4.45

3.66

17.78

3.35

基準穴

=7×2.54mm
25.89

Beam active area(160 x 80 mm2 )25.09

Fiber active region
cross-sectional view
1mm φ

KURARAY SCSF-78M
70
350

Figure 2.8: The structure of BFT

2.4. K1.8 BEAM LINE SPECTROMETER

25

BC3 and BC4
The drift chambers BC3 and BC4 with a 3 mm wire pitch was located at the exit of
the K1.8 beam line spectrometer. Figure 2.9 shows the cell structure of BC3 and BC4.
The sense wire was a gold-plated 12.5 µm diameter tungsten wire and the field wire wasa gold-plated 75 µm diameter copper-beryllium wire. The cathode planes are made of
20 µm-thick graphite pasted on a 12 µm-thick aramid film. The drift chambers have
6 layers (xx′ , uu′ , vv ′ ), where u and v wires were tilted by ±15◦ with respect to the xwires. The wire position of each pair plane was shifted by a half of the cell size. The gas
mixture was Ar(76%)+C4 H10 (20%) + Methylal(4%). The front-end read-out electronics
was made of ASD (Amplifier-Shaper-Discriminator) chips with 16ns integration timedeveloped for ATLAS Thin Gap Chamber. The timing information of the BC3 and BC4
hit was digitized by the COPPER Multi-hit TDC module[54] as described in Chap. 2.6.

Cathode plane
2 mm

Anode

dl1

Potential

Cathode plane
dl2
3 mm

Cathode plane

Figure 2.9: The cell structure of BC3·4

26

CHAPTER 2. EXPERIMENT

Silicon Strip Detector (SSD)
Since there is a 1200 mm distance from BH2 to a target, even if the BC3 and BC4 local
tracking is succeeded, the extrapolated target position is broadened due to multiple
scattering in the BH2 and air between BH2 to the target. Since we use a high intensity
beam, we may have a lot of accidental hits in the tracking detectors with a finite time
resolution, which eventually produce many fake tracks. Also, it is important to have agood vertex resolution to suppress background coming from the materials other than thetarget. Therefore, silicon strip detectors (SSD) with xy structure and 80 µm strip pitch
are installed at the upstream of the target. Figure 2.10 shows a picture of SSD. The
sensor is developed by ATLAS group in LHC. The effective area is 61W ×61H (mm2 ),and thickness is 300 µm. A readout chip, APV25-s1 chip, was developed by CMS groupin LHC. The signal is multiplexed after amplified and shaped, and is transferred seriallyeach 25 nsec (40 MHz clock sampling) to APVDAQ-VME system. APVDAQ system
digitizes the serialized analog data each 25 nsec, and then suppress pedestals within 3σof the pedestal resolution. To reduce the dead time of the data acquisition, a double buffer
mode is applied, which enables us to read and send the data simultaneously. The rate
tolerance was checked at LNS and RCNP test experiment [52]. As shown in figure 2.11,
the efficiency of SSD was kept more than 95% at 105 Hz/strip which corresponds to
2×107 Hz beam at J-PARC.

Figure 2.10: The picture of SSD.

45
(a)
40
35
30
25
20
15
10
5
0

Efficiency [%]Signal-to-Noise Ratio

2.5. SCATTERED-PARTICLE SPECTROMETER (SKS)

103

104

105

Beam Rate / Strip [Hz]

100
(b)
99
98
97
96
95
94
93
92
91
90

103

27

104

105

Beam Rate / Strip [Hz]Figure 2.11: Beam rate dependence of the SSD performances. The horizontal axis represents the incident beam intensity in units of beam rate per strip. The results of the
LNS data are represented by open markers, and the results of the RCNP data are represented by filled markers, where the box and the circle indicate respective SSDs. (a)Signal-to-noise ratio versus beam rate. (b) Hit efficiency versus beam rate.

2.5

Scattered-particle spectrometer (SKS)

The superconducting kaon spectrometer (SKS) was designed and constructed for the
study of Λ-hypernuclei with the (π + , K + ) reaction [36]. Design parameters of the SKS
are summarized in Table 2.4. The characteristic feature of the SKS is to have a good
momentum resolution of 0.1% together with a large acceptance of 100 msr at around 0.9
GeV/c. In addition, it keeps the flight path as short as 5.5 m for the central trajectoryin order to minimize kaon decay-in-flight, and has a powerful kaon identification ability.
The SKS magnetic field is excited at 2.16 T (300A). The SKS enables us to perform
hypernuclear spectroscopy with a good energy resolution and in high statistics.
Table 2.4: Design specifications of the new SKS spectrometer at 2.16 T mode.
Maximum magnetic field
Stored energy
Pole gap
Conductor
Ampere Turn
Maximum current
Total weight
Momentum resolution
Maximum momentum
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
0.1% FWHM at 0.9 GeV/c
1.1 GeV/c
0.70–1.10 GeV/c
85◦ for central trajectory
100 msr∼5.5 m for central trajectory

28

CHAPTER 2. EXPERIMENT

Figure 2.12 shows schematic view of the SKS. The SKS consists of a scintillating fiber
tracker (SFT), three drift chambers (SDC2–4) for the momentum reconstruction, a superconducting magnet, a timing plastic scintillation hodoscope (TOF) and two thresholdtype Čerenkov counters (LAC and LC) for particle identification. The particle momentum was reconstructed with the Runge-Kutta method [61] from the hit information offiber tracker, drift chambers and a calculated field map. 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 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 [55].

SKS
Magnet1m

SDC2
SFT
target

SDC3
SDC4

SSD

BH2
Q13
BC4
BC3

TOF
LAC
LC
Figure 2.12: The schematic view of the SKS. SFT was scintillating fiber tracker. SDC2–4
were drift chambers. TOF was a plastic scintillation counter hodoscope for the Timeof-flight measurement. LAC was aerogel Čerenkov counter (n=1.05). LC was a Lucite(Acrylic) Čerenkov counter (n=1.49).

2.5. SCATTERED-PARTICLE SPECTROMETER (SKS)

29

Trigger counters
Specifications of the trigger counters are listed in Table 2.5. In the trigger, a combinationof three kinds of trigger counters were used to identify pions, kaons and protons. The
TOF counter is sensitive to all charged particles, LAC are sensitive only to pions, andLC is insensitive to protons.
Table 2.5: Specifications of the particle identification counters in the SKS spectrometer
Name Sensitive area
Spec.
PMT
W×H×T (mm)(Hamamatsu)
TOF 2240×1000×30 32 segments
H1949
LAC 1050×1200×113 Aerogel; n=1.05
R1584-02
LC
2800×1400×40 28 segments, Acrylic; n=1.49 H1949, H6410

TOF
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 2.13
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 bysmall transit time spread phototubes (H1949) on the top and bottom sides. The typical
time-of-flight resolution between TOF and BH2 was measured to be 85±6.2 ps (rms).
This is sufficient to separate the scattered pions, kaons and protons.

30

CHAPTER 2. EXPERIMENT

c
XTOF

30 mm

YTOF 70 mm

c1000 mmc

Front viewc

Top view

ZTOF

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 2.13: A schematic view of TOF.
LAC
LAC is a threshold-type silica aerogel Čerenkov counter to reject pions in the trigger
level. As shown in Fig. 2.14, pions with a threshold of 0.45 GeV/c were rejected by
the reflactive index of silica aerogel of 1.05. LAC was installed just behind of the TOF
counter. Figure 2.15 shows a schematic view of LAC. The sensitive area of LAC was
1050×1200×113 mm3 . For the uniform efficiency without any dead space over a large
sensitive area, LAC was not segmented but of a large one-box type. Phototubes whichwere sensitive to a single photon were placed on both sides. The number of photoelectrons was typically 6 over the whole area for scattered pions at 0.9 GeV/c.
LC
LC is a threshold-type Čerenkov counter installed just downstream of LAC. Figure 2.16
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 on the top and bottom sides. In the Acrylic radiator, a wavelength
shifter of bis-MSB was mixed by 10 ppm. On the other hand, due to the scintillatingradiation from the wavelength shifter, several percent of protons were detected below thethreshold. As shown in Fig. 2.14, most of protons slower than 0.85 GeV/c were rejected.

Reflactive index

2.5. SCATTERED-PARTICLE SPECTROMETER (SKS)31

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 2.14: Threshold and refractive index for Čerenkov radiation as a function of the
momentum.

Figure 2.15: A schematic view of LAC.

32

CHAPTER 2. EXPERIMENTc

Top 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 2.16: A schematic view of LC.

Tracking devices
Specifications of the tracking devices in SKS are summarized in Table 2.6.
Table 2.6: Specifications of the tracking devices in the SKS spectrometer.
Name
SFT
SDC2
SDC3
SDC4

Effective area
W×H (mm)
256×150
400×1502140×1140
2140×1140

pitch
(mm)
1.0(xx′ ), 0.75(uv)
5.0
20
20

Wires
xx′ vuvv ′ uu′ xx′
vxuvxuvxuvxuAngle (x, u, v)(◦ )0, +45, −450, +15, −150, +30, −30
0, +30, −30

Typical Resolution(µm in r.m.s)200(xx′ ), 230(uv)
200
300
300

2.5. SCATTERED-PARTICLE SPECTROMETER (SKS)33

SFTThe scintillation fiber tracker (SFT) was newly installed just upstream the target. SFT
has a xx′ vu structure. The x and x′ planes have a similar structure of BFT. The v andu planes tilted by 45 degrees are made of small scintillating fibers with 0.5 mm diameterto reduce materials as much as possible. For v and u planes, one MPPC reads out threebundled fibers to reduce the readout channels. The same read-out electronics was thosefor BFT was used.
Fiber reflection edge

Position pin
25.09

25.89
4.49

4

120°

45°

160

450

MPPC sensor area

0.5

0.51

0.5

LED

280

0.5 mm φ74
570
LED導入口

3 fibers are readby the same MPPC

Figure 2.17: Schematic view of SFT.

SDC2
SDC2 is a drift chamber installed downstream of the SFT. The anode wire pitch of the
SDC2 was 5 mm. The wire configuration of the SDC2 was vv ′ uu′ xx′ , where u and v
wires were tilted ±15◦ with respect to the x wires. The sense wire was gold-plated 12.5
µm 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 carbon pasted on a 12
µm thick aramid film. The gas mixture and read-out electronics were the same as thoseof BC3 and BC4.

34

CHAPTER 2. EXPERIMENT

SDC3 and SDC4
SDC3 and SDC4 are located at the exit of SKS. The size of the effective area was
2140×1140 mm2 . The anode wire was a gold-plated 25 µm diameter tungsten wire, andboth field wire and cathode wire were gold-plated 80 µm diameter copper-beryllium wire.
The pitch of the cathode wires was 2 mm. SDC3 and SDC4 have vxuvxu configuration,
where u and v wires were tilted ±30◦ with respect to the x wires. The gas mixture
was Ar(50%) + C2 H6 (50%). The frond-end read-out electronics of SDC3 and SDC4 wasmade of ASD chips. The timing information of the SDC3 and SDC4 hit was digitizedby the TKO Dr.TII TDC module as described in Sec 2.6.

C athode (GND)
P otential (-450V)
P otential (-350V)

12 mm
Anode (~+2200 V)

Drift length

P otential (-450V)

20 mm

Figure 2.18: The cell structure of SDC3·4

2.6. TRIGGER

2.6

35

TriggerIn the (π − , K + ) reaction, many background particles are produced through the pionnucleus reactions, such as (π, p)X and (π, π)X. Especially, protons produced from π − p →π − π 0 p reaction is a main background in the SKS momentum acceptance because the crosssection is 103 times larger than that for the (π − , K + ) reaction. Therefore, a powerful(π − , K + ) trigger system is very important. In the present system, the 1st level (π, K)
trigger, TOF–LC matrix trigger and the 2nd level mass-trigger systems are introduced.
Prescaled beam trigger and (π, π) trigger was mixed into them.

The 1st level (π, K) trigger
The 1st level (π, K) trigger was comprised of four kinds of counters, BH2, TOF, LAC
and LC, and defines as:
P IK ≡ BH2 × T OF × LAC × LC
BH2, TOF, and LC had two PMTs at both ends, and mean timer modules were used
to remove the incident position dependence of the trigger timing. The PIK trigger logic
diagram is shown in Fig. 2.19.
The BH2 timing was used as the STOP signal of the TDC’s for BFT, BC3, BC4,
SFT and SDC2, while the TOF timing was used as stop for SDC3,4 because the flighttime from BH2 to TOF varies a lot depending on the different flight paths and momentaof scattered particles.

1st level
PIK Trigger

Mass Trigger
System

1st level clear

LAC
LAC
LAC

Figure 2.19: PIK trigger logic diagram.

2nd level
PIK Trigger

36

CHAPTER 2. EXPERIMENT

Beam and (π,π) trigger
The 1st level beam and (π, π) trigger are defined as,
BEAM ≡ BH2
P IP I ≡ BH2 × T OF × LC
These triggers are mixed in the (π, K) trigger with prescale factors to monitor eachcounter’s efficiency and to adjust calibration parameters for detectors. The prescale
factor is 1/(256×256×4) in the beam trigger and 1/300 in the (π, π) trigger, respectively.

Matrix trigger with LC and TOF

LC segment #In high rate pion beam experiments, many of particles scattered at other materials suchas SKS yoke and beam line Q-magnets hit the TOF and LC, and make fake triggers. To
reduce such fake triggers, a matrix trigger is introduced.
The matrix trigger is generated when the appropriate hit combinations between TOF
and LC segments are matched. For constructing the matrix trigger, we used an FPGA
module called TUL (Tohoku Universal Logic Module) [56]. Figure 2.20 shows the selectedcombinations of the TOF and LC segments. In the figure, the selected region is indicatedby solid lines and the background events are located out of the region. The 1st level(π, K) trigger is reduced by 10% with the matrix trigger.

25
20
15
10
5
0
0

5

10

15

20

25
30
TOF segment #Figure 2.20: 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.

2.6. TRIGGER

37

The 2nd level mass trigger
The outgoing particles are roughly identified from the difference of time-of-flight byselecting hit combination of TOF and LC. The particle identification can be done bysetting a suitable window against time-of-flight of TOF.
The trigger scheme for the mass trigger is illustrated in Fig. 2.21. The timing information of the TOF signals were 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 sends the 4 bit of hit address information and 9 bit of time-of-flightinformation to TUL. Hit information of TOF and LC, and time-of-flight information ishandled in the TUL module. If the time-of-flight of TOF is in the time window we set,the 2nd level (π, K) trigger is generated. If not, the 1st trigger clear signal is generated
and all the stored data in each DAQ modules is cleared. The decision time of the mass
trigger was about 15 µs. In the present experiment, 60% of the 1st level (π, K) triggers
are rejected.

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 2.21: Logic Scheme of the mass trigger.

38

2.7

CHAPTER 2. EXPERIMENT

Data-acquisition system

Figure 2.22 shows a diagram of the data-acquisition system. The raw signals of trigger
counters and SDC3 and SDC4 were digitized with the TKO high resolution TDC and
ADC modules and the TKO TDC (Dr.TII) modules [57], respectively. For the TKO
modules, the digitized signals were transferred to the VME-SMP (Super Memory Partner), which was installed in the VME box together with a VME-CPU module. Then, thedata were read out by the VME-CPU (V7807RC) module and transferred to the hostcomputer.
The timing information of the BC3·4 and SDC2 was digitized by the FINESSE Multihit TDC installed in the COPPER modules. COmmon Pipelined Platform for Electronics
Readout(COPPER) [54] is a new platform module for the KEK-VME specification thatrealizes various types of analog-to-digital conversion and pipelines digital data processing
functions in a unified scheme. The MHTDC module encoded the timing information
with an accuracy of 1 ns. The BC3, BC4 and SDC2 data on the COPPER modules weredirectly transferred to the host computer by the SiTCP connection. The data-acquisition
cycle was processed event by event.
The timing information of the BFT and SFT was digitized by the EASIROC Multi-hit
TDC [53]. EASIROC is developed by Linear Accelerator Laboratory (LAL) in France.
EASIROC has many functions such as amplifier, shape EASIROC chip digitized leading
and trailing edge as time-over-threshold with an accuracy of 1 ns. Since the EASIROC
board does not have CPU, data acquisition is controlled by daughter computer with
SiTCP communication. The data were transferred to host computer via the daughtercomputer.
The signal from SSD was digitized by the FADC system (APVDAQ). At first analog
signal is multiplexed by the APV25 chip mounted on the SSD board, then the serialized
signal transferred to FADC VME module (APVDAQ) via a CAT7 Ethernet cable every
25 ns. APVDAQ digitizes the analog signal, and transfers it to the VME-CPU controller(XVB601).
For building up an event by combining data sets coming from the different modules,
we need 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 have developed a trigger/tag distribution system. When the trigger signal was generated, theMaster Trigger Module (MTM) accepted the trigger signal and distributed the eventand spill numbers to Receiver Modules (RM) in each node by using Ethernet cables.
After finishing the analog 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 eventand spill numbers were transferred 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
were transferred together with the digitized raw data to the host computer.
The data transferred from each module to the host computer were at first processedby the Event-Builder. Then they were transferred to the Event-Distributor and to HDD
data storage as well as to the on-line analyzer.

2.7. DATA-ACQUISITION SYSTEM

39

APV DAQ
VME-RM

EASIROCEASIROCFERA-RM

Figure 2.22: Diagram of the data-acquisition system.

40

2.8

CHAPTER 2. EXPERIMENT

Lithium-6 target

An enriched 6 Li target (95.54%) of 3.5 g/cm2 in thickness and 70W ×40H (mm2 ) in size
was used as shown in Fig 2.23. The typical beam profile, 56W ×28H (mm2 )(FWTM), is
fully covered with the target. Although, it is the best preservation way to use alminium
laminated package in order to suppress the oxidization of Lithium, we are not able tomonitor where the Lithum is located. Therefore, we use (Z-86) bag [58] so that we could
monitor the position.
Z-86 has a low rate of the oxygen transmission (80 ml/m2/MPa at 20C◦ ) and a
two-layer structure of polyethylene, oriented polypropylene coated with polyvinylidene
chloride. The thickness was 55 µm. The 6 Li target was doubly packed with Z86 in the
Argon gas grove box. Before and after the experiment, we checked oxidization of 6 Li,
and there was no oxidization of surface at visual monitoring level.

Figure 2.23: The Picture of 6 Li target

2.9. DATA SUMMARY

2.9

41

Data summary

The 6Λ H production data by the 6 Li(π − , K + ) reaction were taken in two cycles in December 2012 and in January 2013 as listed in Table 2.7. The total number of pions irradiatedon the 6 Li target was 2.1 × 1012 . At first, we took 12Λ C production data to evaluate themissing-mass resolution. Next, we made measurements of the Σ− and Σ+ production
reaction from hydrogen on a (CH2 )n target at a beam momentum of 1.377 GeV/c. We
also performed the beam-through runs at four momentum settings, 0.8, 0.9, 1.0 and 1.2
GeV/c, with and without the 6 Li target to evaluate the amount of energy straggling andthe energy loss in the target.
Table 2.7: Summary of runs. Target material and thickness, and beam momentum andintensity are listed.
targetbeam
runmaterial thickness
momentumintensity
irradiated2(g/cm )
(GeV/c)(pion/spill)pion
66Li(π − , K + )
Li
3.5
1.2
1.2–1.4 × 107 2.1 × 101212C(π + , K + ) graphite
3.6
1.2
4.1 × 106
5.4 × 1010−+−7p(π , K )Σ(CH2 )n3.4
1.377
1.3 × 10
4.1 × 1010p(π + , K + )Σ+ (CH2 )n
3.4
1.377
3.5 × 106
3.1 × 109
beam-throughnone
0.8, 0.9, 1.0, 1.2∼ 104

Chapter 3
Data Analysis
3.1

Outline

The mass of the produced particle (M ) was obtained as a missing mass in the (π, K)
reaction fromq
M = (Eπ + MA − 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 ofa kaon, MA is the mass of a target nucleus, and θπK is the scattering angle.
The beam momentum and kaon momentum were reconstructed from the tracking
information on BFT, BCs, SFT and SDCs. At the first stage of the tracking analysis,straight-line track candidates were determined both at the entrance and the exit of thespectrometer system. Then the best track candidates were selected from the combination of the straight-line tracks so as to give the least chi-squares in the momentum
reconstruction. For the track reconstruction of K1.8 beam line spectrometer, a beamtransport matrix in third-order was used. In the track reconstruction of SKS, a calculated field map was used, and the SKS track was reconstructed with the Runge-Kutta
method. After the track reconstruction, the identification of kaon was carried out by using the time-of-flight between BH2 and TOF with the flight path and the reconstructed
momentum of SKS. Then, a vertex point of the (π, K) reaction event was reconstructedfrom the trajectories of pion and kaon, and finally the missing mass was obtained.

42

3.2. ANALYSIS OF BEAM

43

3.2

Analysis of beam

3.2.1

Identification of triggered beam particles

At first, incident hadron beam such as pion, kaon and proton was separated with theelectro static separator (ESS1,2) as already shown in Fig.2.3. The contamination of
proton and kaon was negligibly small. However, light lepton particles such as electron
and muon can not be rejected with ESS. The contamination of electron was estimatedwith GC hits at low intensity beam and the contamination of muon was estimated fromthe Decay TURTLE simulation [59]. The details are described in Chap. 4.2.1. An
incident triggered beam was selected by a time window of 2 ns in the BH2 hits as shownin Fig 3.1. The ratio of single hit of BH2 within the 2 ns was estimated to be 91.0±2.0%.
In present analysis, we selected only single hit of BH2 as triggered segment.

70000
60000
50000
40000
30000
20000
10000
0
-5

-4

-3

-2

-1

0

1

2 3
4 5
BH2 Time [ns]Figure 3.1: Typical BH2 time spectrum of the incident beam particles. The selected
time window was indicated by arrows.

3.2.2

BFT analysis

The timing information of BFT was digitized by the EASIROC multihit-tdc by the
sampling time interval of 1 ns (1 GHz sampling). In the digitization, both leading edge
and trailing edge information of raw signals were taken as time over threshold (TOT).
The time resolution of BFT can be improved with the time walk correction by using the
TOT. Figure 3.2 shows the correlation of the TOT and time before the correction. The

44

CHAPTER 3. DATA ANALYSIS

100
80
(a)
60
40
20
0
-20
-40
-60
-80
-100
0 10 20 30 40 50 60 70 80 90 100
TOT [ns]

Time [ns]Time [ns]time is corrected with a 2nd-order poly-nominal function. After the correction, the time
resolution is found to be 1.12 ± 0.03 ns.

100
80
(b)
60
40
20
0
-20
-40
-60
-80
-100
0 10 20 30 40 50 60 70 80 90 100
TOT [ns]

Figure 3.2: Slewing correction of BFT.

CountsFigure 3.3 shows the time projection of Figure 3.2(b). In the present analysis, thetime gate with a ±3 ns width was set as indicated by arrows. When there were hits on

10000
8000
6000
4000
2000
0
-50

-40

-30

-20

-10

0

10

20

30
40
50
BFT Time [ns]Figure 3.3: Typical TDC distribution of BFT. The Tdc distribution was the sum of all
hits in a fiber. All multi-hit signals were shown in the distribution.
adjacent fibers whose signal is matched each other within the ±3 ns time gate, thosefibers were made up into a cluster. For the tracking analysis, the position of the central
fiber in the cluster was used.

3.2. ANALYSIS OF BEAM

3.2.3

45

BC3 and BC4 local tracking

BC3 and BC4 drift length calculation

CountsFor the position calibration of BC3 and BC4, at first, the TDC information was converted
to the drift time information. Figure 3.4 shows a typical TDC distribution for one of
the BC3 and BC4 layers. A bump structure in the tail of the distribution was causedby satellite signals due to the ringing in the ASD card. Those satellite signal eventswere rejected in the tracking process because the timing of the satellite signals was far
from the drift time range and their coincidence rate was quite low. The flat background
distribution was caused by accidental events due to high intensity beam pions. The
25000
20000
15000
10000
5000
0
580

600

620

640

660

680

700

720

Tdc Channel

Figure 3.4: Typical TDC distribution of one of BC3·4 layers. The TDC distribution was
the sum of all hits in a layer, and all multi-hit signals were shown in the distribution.
origin of the drift timing was roughly determined with the edge of the TDC distribution(about 700 ch in Fig. 3.4) and the TDC channels were converted to the drift time using
the MHTDC channel width of 1 ns. The conversion function from the drift time to drift
length was obtained with the following equation by assuming the uniform hit distribution,
Rt
dtDT (t)t0× max drif t length,(3.1)
DL(t) = R tmax
dtDT (t)t0where t0 is the time origin, tmax is the maximum dift time for the maximum drift length,and DT (t) is the observed drift time distribution.
Figure 3.5 shows a scatter plot between the drift time and the drift length (DL(t))
for one of the BC3 and BC4 layers. The scatter plot was fitted by using a 5th-orderpolynomial function. This function was optimized in iteration.

CHAPTER 3. DATA ANALYSIS

Drift length [mm]

46

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 3.5: 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.
Table 3.1: The position resolution of each layers.
BC3-Layer resolution [µm] Layer
resolution [µm]BC3-x210 ± 0.4BC4-u
197 ± 0.4′′BC3-x
200 ± 0.4BC4-u
196 ± 0.4
205 ± 0.5BC4-v
203 ± 0.5
BC3-u
BC3-u′
203 ± 0.4
BC4-v ′
205 ± 0.5BC3-v
196 ± 0.4BC4-x
213 ± 0.7
BC3-v ′
208 ± 0.5
BC4-x′
219 ± 0.7
Local straight track search
In finding BC3 and BC4 tracks, all combination of all the hit positions in each layer were
examined. Those local straight tracks were found by using the least squares method. The
local position coordinate was shown in Fig. 3.6. For the origin of the local coordinate,
we defined optical focal points as VI and VO. The VI is the position of BFT and theVO is 130 mm downstream of the end-guard of the exit Q-magnet (Q13). The locationof the VI and VO points were shown in Fig. 3.7.
The track parameters (x0 , y0 , u0 (dx/dz), v0 (dy/dz) and the drift direction (L/R)
were obtained for a local track candidates giving the least χ2 . Figure 3.8(b) shows a χ2
distribution of the BC3 and BC4 tracking. In the local track search, the tracks were
accepted to be less than 30 of the χ2 value. Figure 3.8(a) shows a residual distribution of
one of the BC3 and BC4 layers. In the calculation of the residual distribution, the calculated layer was not included in the tracking analysis. The obtained position resolutionof each layer is listed in Table. 3.1.

3.2. ANALYSIS OF BEAM

47

Drift chamber
Beam(Z direction)

Y (Vertical)

X (Horizontal)
Particle
trajectory

Hit wire
WP

Drift chamber origin(Central wire position)

Figure 3.6: Local position coordinate for the local straight tracking.

z
x

y

5m

VO

BH2
BC4
BC3

Q13
Q12

x

D4
z

y

VI
GC

BFT

Q10 Q11

Figure 3.7: The VI and VO point in the K1.8 beam line spectrometer. The position of
VI and VO which were the origin of the local coordinate.

48

CHAPTER 3. DATA ANALYSIS

12000

4000

(a)

3500
3000

(b)

10000
8000

2500
2000

6000

1500

4000

1000
2000

500
0
-1.5

-1

-0.5 0 0.5 1 1.5
BC3&4 residual [mm]

0
0

5

10

15

20

25

30

χ2 of BC3&4 tracking

Figure 3.8: (a) Typical residual distribution of one of the BC3·4 layers. (b) Typical χ2
distribution of the BC3·4 tracking.

3.2.4

Beam momentum reconstruction

The beam momentum was analysed from the hit position information of BFT and the
local track information of BC3 and BC4 by using the 3rd-order transport matrix M
calculated with the ORBIT code [60] as follows,~ in = M (X~ out , δ),X
dxin dyin
X~in = (xin , yin ,
,
).
dz dz
dxout dyout,),
X~out = (xout , yout ,dz
dz~ in and X~ out are the horizontal and vertical positions and their derivatives at thewhere X
entrance (VI) and the exit (VO) of the K1.8 beam line spectrometer and δ is momentum
deviation from the central momentum denoted as p = p0 (1 + δ), where p0 is the central~ in from the hit information of
momentum. Since we have only one information xin in X~
BFT, a third-order polynomial equation xin = f (Xout , δ) was used to estimate the δ.
In the ORBIT code, the properties of the K1.8 beam line spectrometer magnets, theeffective magnetic length, aperture, field strength of the central ray, and bending angle
and the radius of central orbit for the dipole magnet are inputs. The effective magnetic
length was determined from a measured magnetic field distribution. The aperture wastaken from the design value of the spectrometer magnets. The properties of the magnetic
fields of all the magnets were also calculated by using the excitation curve.
Figure 3.9 shows a beam momentum distribution for 6 Li(π − , K + ) production runs.
The single track events were selected. The momentum bite was typically ±2%. The
momentum distribution depends on the slit condition. The slit condition in the present
experiment was listed in Table 3.2.

Counts

3.2. ANALYSIS OF BEAM

49

16000
14000
12000
10000
8000
6000
4000
2000
0

1.17

1.18

1.19

1.2

1.21

1.22 1.23 1.24 1.25
Beam Momentum [GeV/c ]Figure 3.9: Typical distribution of the beam momentum at 1.2 GeV/c

Table 3.2: Slit condition of 6 Li(π − , K + ) production reaction
Slitupper [mm] lower [mm]
IFH
+70
-70
IFV
+2.6
-1.0
Mom
+60
-60
1st mass slit
+1.69
-1.69
2nd mass slit
+1.76
-1.76

50

CHAPTER 3. DATA ANALYSIS

0.2

BFT U

BFT V

The other parameters, yin , dxdzin and dydzin of X~in are also obtained in reconstructing the
momentum. Figure 3.10 shows typical beam profile in vertical and horizontal at VI. The
events within the indicated arrows are accepted as good beam pion tracks to suppressthe π → µ decay events.

0.15

0.2
0.15

0.1

0.1

0.05

0.05

0

0

-0.05

-0.05

-0.1

-0.1

-0.15

-0.15

-0.2
-100 -80 -60 -40 -20 0

20 40 60 80 100
BFT Y[mm]-0.2-100 -80 -60 -40 -20 0

20 40 60 80 100
BFT X[mm]Figure 3.10: Typical distribution of XY and UV at BFT calculated from δ3.3. ANALYSIS OF SCATTERED PARTICLES

3.3

Analysis of scattered particles

3.3.1

Hodoscope cut

51

In order to reduce background particles and the analysis time, hodoscope cuts wereapplied to TOF-ADC before local straight tracking. Large ADC hits in TOF were
rejected as proton like events. The ADC cut region was set for each segment according
to a simulation. In this cut, 10% of all events are rejected.

3.3.2

SFT and SDC2 local tracking

The hit information of SFT was selected in the time window with ±3 ns after slewing
correction in the same way as BFT analysis. When there were hits on adjacent fibers,
those fibers were made up in to a cluster within the maximum cluster size of three. The
hit information of SDC2 is obtained in the same method as in BC3 and BC4.
In finding SFT and SDC2 local tracks, all combinations of all the hit positions in eachlayer were examined. Those local straight tracks were found by using the least squares
method. The minimum number of planes was required to be seven.
Figure 3.11 (a) – (c) shows a typical residual distribution of SFT and SDC2 tracking
of SFT-X layer (a), SFT-U layer (b) and one of the SDC2 layer (c). The position
resolution was 200 µm in SFT-X, 230 µm in SFT-UV and 200 µm in SDC2, respectively.
In the local track search, the accepted χ2 value was selected to be less than 30 as shownin Fig. 3.11(d).

3.3.3

SDC3 and SDC4 local tracking

The hit information of SDC3 and SDC4 was obtained with the same method as in BC3,
BC4 and SDC2. For the SDC3 and SDC4 tracking, all combinations of all the hit
positions in each layer were examined. The minimum number of planes was required tobe nine. Figure 3.12 shows a typical residual distribution of one of the SDC3 and SDC4
layers. The position resolution was 300 µm. In the local track search, the accepted χ2value was selected to be less than 20.

3.3.4

Momentum reconstruction of a scattered particles

The momentum of the scattered particle was determined by reconstructing a trajectory from the hit positions. The reconstruction was carried out with the Runge-Kutta
method [61] for each particle using a calculated magnetic field map. The magnetic field
map was calculated with the ANSYS code. The trajectory and the momentum were
optimized by minimizing the following χ2 values iteratively.
!2n
1 X xtracking− xdataii2χsks ≡,n − 5 i=1
wiwhere n is the number of the chamber planes with a hit, xtracking
and xdata
are the hitiiposition on the i-th plane in the tracking in and the data, and wi is the position resolutionof the i-th plane.

5000

(a)

4000

CountsCHAPTER 3. DATA ANALYSISCounts

52

(b)

2500
2000

3000
1500
2000

1000

1000
0
-2 -1.5

500

-1

-0.5

0
-2 -1.5

0 0.5 1 1.5 2
SFTX Residual [mm]

-1

-0.5

0 0.5 1 1.5 2
SFTU Residual [mm]

(c)

3000

CountsCounts

10000

(d)

8000

2500
6000

2000
1500

4000

1000
2000
500
0
-2 -1.5-1-0.5

0 0.5 1 1.5 2
SDC2 Residual [mm]

0
0

5

10

15
20
25
30
SFT&SDC2 tracking χ2

Figure 3.11: Typical residual and χ2 distributions of SFT·SDC2 local tracking. (a) shows
the residual of SFT-X, (b) shows the that of SFT-U and (c) shows the that of one of the
SDC2 layer. (d) shows the typical χ2 distribution.

53

CountsCounts3.3. ANALYSIS OF SCATTERED PARTICLES

7000
6000

104

5000

Accepted
3

10

4000
3000

102

2000
10

1000
0
-1.5

-1

-0.5

0
0.5
1
1.5
SDC3 Residual [mm]

0

5

10

15
20
25
30
χ2 of SDC3&4 tracking

Figure 3.12: Typical residual distribution of one of the SDC3·4 planes (left), and χ2
distribution of SDC3·4 (right).
The fitting parameters were the momentum (p), the horizontal (x) and vertical (y)positions and their derivatives (dx/dz, dy/dz) at the target position. In the present
analysis, the initial momentum was set at 0.9 GeV/c. In the local tracking in SFTSDC2 and SDC3-SDC4, a straight track was assumed. However, there is a small effectof the fringing magnetic field of SKS. Therefore, in the SKS tracking the full tracking
using the field map was performed by considering the fringing field. The track parameter
optimization was repeated iteratively until the χ2 reaches a convergence criteria. The
convergence criterion in the iteration is δχ2 = (χ2k+1 − χ2k )/χ2k < 10−3 , where k is thenumber of iteration and χ2k is the tracking χ2 for the k-th iteration.
Figure 3.13 shows a typical χ2 distribution in the SKS tracking. The χ2 is selectedless than 10.

CHAPTER 3. DATA ANALYSISCounts

54

7000
6000
5000
4000
3000
2000
1000
0
0

5

10

15

20

25

30

35 40 45 50
χ2 of SKS tracking

Figure 3.13: Typical χ2 distribution of SKS tracking.

3.3.5

Particle identification in the SKS spectrometer

The PIK trigger cannot completely remove all the background. The background particles
were fast protons which fired LC and were misidentified as kaons and pions which were
not rejected by LAC due to its inefficiency. After the Runge-Kutta tracking, the massof a scattered particle (Mscat ) was finally obtained as
Mscat =

pp
1 − β 2,β(3.2)

where β is the velocity of a scattered particle obtained from the time-of-flight and theflight path length, and p is the momentum obtained from the SKS tracking. Figure 3.14
shows a typical mass squared spectrum for the 6 Li(π − , K + ) reaction with χ2sks < 10 and
0.7 < p < 1.2 GeV/c cut. A tail in the low mass side of the proton distribution is missuse of timing information of BH2. Very high intensity beam causes accidental hits after
the true start timing. If the accidental hit timing was used for the β calculation, it
produce the slow component. Around the kaon region (0.2 < m2 < 0.3) is overlapped
the proton tail. Also a pion tail is overlapped because of the resolution of mass squaredof pion. Since mass squared resolution depends on momentum, momentum dependent
cut with 2σ of mass squared resolution is applied to select kaons as shown in Fig. 3.15.

Counts

3.3. ANALYSIS OF SCATTERED PARTICLES

105
10

π

4

K

55

p

103
102
10
1
-0.2

0

0.2
0.4
0.6
0.8
Mass Squared [(GeV/c)2]

1

1.2

Figure 3.14: Scattered particle mass squared distribution for the 6 Li(π − , K + ) data

Mass Squared [(GeV/c2)2]

1.2
1

p

0.8
0.6
0.4
0.2
0
-0.2

K+

π+
0.6

0.8
1
1.2
Momentum [GeV/c]

1.4

Figure 3.15: Mass squared vs. momentum plot of the scattered particles measured by
the SKS spectrometer in the 6 Li(π − , K + ) reaction. Two curves in the figure show the
momentum dependent 2σ cut for the kaon selection.

56

CHAPTER 3. DATA ANALYSIS

3.4

Vertex reconstruction

The scattering angle and the vertex point were obtained from both incident beam andscattered particle trajectories which were obtained by the track reconstruction in theK1.8 beam line spectrometer and the SKS, respectively. Especially, incident beam track
was corrected by using the SSD hit position. Since there was material of BH2 between
the target and BC4, angle resolution and vertex resolution were worse because of themultiple scattering effect. Correction Step is as follows,
1. Calculate the hit position at BH2 by extrapolating the BC3-4 track.
2. Calculate the angle from hit position of BH2 and SSD.

600

(a)

500

CountsCountsFigure 3.16 shows a typical distribution of the horizontal (a) and vertical (b) scattering
angle difference measured by both spectrometers for the beam-through data with theπ − of 0.9 GeV/c in empty target data. We obtained the horizontal and vertical angularresolutions of 2.13 ± 0.01 mrad and 2.11 ± 0.01 mrad in σ, respectively.
600

(b)

500

400

400

300

300

200

200

100

100

0
-0.03 -0.02 -0.01
00.01 0.02 0.03
Horizontal angle difference [rad]0-0.03 -0.02 -0.01
00.01 0.02 0.03
Vertical angle difference [rad]Figure 3.16: Typical distribution of the horizontal (a) and vertical (b) scattering angle
difference measured by both spectrometers for the π − of 0.9 GeV/c in empty target data.
The horizontal and vertical angular resolutions were 2.13 ± 0.01 mrad and 2.11 ± 0.01
mrad in rms, respectively.
The reaction vertex point was obtained from the closest distance between the tracks
of beam pion and scattered kaon. Figure 3.17 shows a distribution of the vertex position
and the closest distance for the 6 Li(π − , K + ) production data, where z-axis was definedas the beam direction. The vertex cut region in z-direction is selected less than the realtarget length +20 mm, and in x- and y-direction is selected smaller than the real target
size. The good vertex event is selected less than 5 mm in the closest distance.

500

1400

target

(a)

450
400

57

CountsCounts

3.4. VERTEX RECONSTRUCTION

350

1000

300

800

Accepted

250

target

1200

200

600

150

400

(b)
Accepted

100
200

50

Counts

3000

-200

-100

0

20 40 60 80 100
Vertex X [mm]1800target2500

0-100 -80 -60 -40 -20 0

100 200 300
Vertex Z [mm]Counts

0
-300

(c)

Accepted

1600

(d)

1400
2000

1200
Accepted

1500

1000
800

1000

600
400

500

200
0
-100 -80 -60 -40 -20 0

20 40 60 80 100
Vertex Y [mm]

0
0

2

4

6

8

10 12 14 16 18 20
Closest Distance [mm]Figure 3.17: Distributions of vertexes and a closest distance. (a) shows a vertex distribution of z-direction, (b) shows that of x-direction and (c) shows that of y-direction. (d)shows a distribution of closest distance.

58

3.5

CHAPTER 3. DATA ANALYSIS

Analysis of the beam-through runs

Counts/0.1 MeV/c

The beam-through runs are taken in four momentum settings at 0.8, 0.9, 1.0 and 1.2
GeV/c. During the runs, the SKS magnet was set at the negative polarity of 2.16 T.
Figure 3.18 shows a distribution of the difference of momenta between the beam line
spectrometer and the SKS spectrometer at a momentum of +0.9 GeV/c.

800
700
600
500
400
300
200
100
0
-4

-2

0

2

4

6

∆P=p

8
-p

K1.8

10
12
[MeV/c ]SKS

Figure 3.18: The momentum difference between the two spectrometers without any offset
correction. The beam momentum setting was 0.9 GeV/c
Figure 3.19 shows the width of the distribution for the momentum difference between
two spectrometers (∆p) as a function of the nominal central momentum of the beam line
spectrometer. This width comes from the momentum resolution of the two spectrometers12
2(σK1.8 and σsks ) and is given as σ∆p = (σSKS+ σK1.8) 2 . The width is ∼0.2% (FWHM)
at 0.8 GeV/c, and proportionally increases as the momentum.

Momentum Width [MeV/c]

3.6. MOMENTUM CORRECTION

59

3.6
3.4
3.2
3
2.8
2.6
0.8 0.85 0.9 0.95

1 1.05 1.1 1.15 1.2
Central Momentum[GeV/ c]

Figure 3.19: The width of the distribution for the momentum difference between the two
spectrometers as a function of the central momentum of the beam line spectrometer.

3.6

Momentum correction

3.6.1

Overview

Momentum correction is taken into account for both incoming pion and outgoing kaon.
At first, we consider the energy loss of the target and BH2. For beam pion momentum,
since measured momentum is before BH2 and target, momentum is corrected at reaction
vertex point.

3.6.2

Momentum correction of scattered particles

In the present experiment, the momentum of the scattered particles was reconstructed byusing the calculated magnetic field map. However, the present magnetic field map does
not completely reproduce the real magnetic field, especially, in fringing fields. This effectcan be seen by checking the dependence of missing mass on scattering angle. Figure 3.20
shows a scatter plot between the missing-mass for the p(π ± , K + )Σ± reaction and thederivatives of horizontal (dx/dz) or vertical (dy/dz) directions at the target point. The
higher order correlation between the derivatives and the missing mass is seen in the figure(a, b).
To optimize the energy resolution, this correlation was corrected in the SKS momentum with the derivatives of the horizontal and vertical positions. For the correction, themomentum difference (Pcalc − Panalyzed ) was used. The analyzed momentum (Panalyzed )was obtained from the momentum reconstruction by the SKS tracking. This momentum
should have some correlation with the derivatives. The calculated momentum (Pcalc ) was
obtained from the calculation by the scattering angle and the beam momentum, whereMissing Mass

CHAPTER 3. DATA ANALYSIS

Missing Mass

60

1.22

1.22

(a)
1.21

(b)

1.21

1.2

1.2

1.19

1.19

1.18

1.18

-0.3 -0.2 -0.1

0

0.1

0.2

0.3

-0.1

-0.05

0

0.05

Missing Mass

Missing Mass

dx/dz

1.22

1.22

(c)

1.21

(d)

1.21

1.2

1.2

1.19

1.19

1.18

1.18

-0.3 -0.2 -0.1

0.1
dy/dz

0

0.1

0.2

0.3

dx/dz

-0.1

-0.05

0

0.05

0.1
dy/dz

Figure 3.20: A scatter plot between the derivatives of horizontal (dx/dz) or vertical(dy/dz) positions at the target point and the Σ− missing-mass. The figures after corrected for the correlation are shown in (c, d)3.6. MOMENTUM CORRECTION

61

the kinematics of the p(π ± , K + )Σ+ reaction was assumed. This momentum has no correlation with the derivatives. Thus, the subtraction (Pcalc − Panalyzed ) has the informationof the correlation. The correction for the SKS momentum was made with the 3rd-orderpoly-nominal in dx/dz and 2nd-order poly-nominal in dy/dz, respectively. In the sameway, the SKS momentum was also corrected for the bound region in 12 C(π + , K + )12
ΛC
production.

62

3.6.3

CHAPTER 3. DATA ANALYSIS

Target energy loss and straggling

In order to examine the effects of the target energy loss and its straggling, π + beamthrough data without and with a target were taken at 0.8, 0.9, 1.0 and 1.2 GeV/c. As an
example, Figure 3.21 shows a distribution of the momentum difference measured by thebeam spectrometer and the SKS without(a) and with(b) the (CH2 )n target (3.4 g/cm2 )for a 0.9 GeV/c π + beam. The energy loss was obtained as the shift of the centroid. Theenergy straggling was obtained from the difference of the widths. The results of energy
loss and straggling are summarized in Table 3.3. The obtained values are consistent
with Bethe-Bloch formula within 0.1 MeV, which is better enough as compared withmissing-mass resolution. Therefore, the energy loss was corrected by using Bethe-Blochformula for 6Λ H, Σ± , and 12Λ C production runs. Once the missing-mass is reconstructed,
the event-by-event correction of the target energy loss was applied according to vertex
position.
Table 3.3: target energy loss and stragglings
momentum energy loss
straggling(MeV)
FWHM(MeV)(GeV/c)0.8
6.48±0.14
1.39±0.23
0.96.47±0.18
1.31±0.24
1.0
6.92±0.34
1.45±0.22
1.2
7.08±0.29
1.23±0.18

Counts/0.1 MeV/ c

3.6. MOMENTUM CORRECTION

63

800
(a)

700
600
500
400
300
200
100

Counts/0.1 MeV/ c

0

0

5

10

15
20
∆P=pK1.8-pSKS [MeV/c]

600
500

(b)

400
300
200
100
0

0

5

10

15
20
∆P=pK1.8-pSKS [MeV/c]

Figure 3.21: Distributions of the momentum difference between the two spectrometers
without(a) and with(b) the (CH2 )n target(3.4 g/cm2 ) for a 0.90 GeV/c π + beam. In(b), centroid is shifted and the width is widened because of the target energy loss andits straggling.

64

3.6.4

CHAPTER 3. DATA ANALYSIS

Momentum correction of beam pions

The momenta of particles measured in the K1.8 beam line spectrometer were correctedwith a 1st-order poly-nominal function by considering the results of the beam-throughrun at 0.9 GeV/c and p(π − , K ± )Σ± runs at pπ = 1.38 GeV/c. Since the SKS magnetic
field is fixed in all runs, the momentum of scattered particle measured in the SKS spectrometer is not corrected (As mentioned in Sec 3.6.2, only scattering angle dependency
was corrected). The momentum difference between K1.8 and SKS (dp = psks − pK1.8 )was measured -2.43 MeV/c from the beam-through run at 0.9 GeV/c by considering
the energy loss of BH2. In the Σ± production runs the mass difference of Σ+ (Σ− )(Mmeasure−Σ − MP DG−Σ ) was found to be +1.18 MeV/c2 (+0.28 MeV/c2 ). A momentum
offset of +1.74 MeV/c is estimated from the deviation of the measured Σ+ mass at 1.38
GeV/c from the PDG value. The effect of the beam polarity change from π + to π − isestimated to be -1.30 MeV/c from the peak positions of Σ+ and Σ− in the missing-mass
spectra. After all, the beam momentum was corrected with a 1st-order poly-nominal
function of the measured beam momentum (p−K1.8 ) as follows,−p−
corrK1.8 = 1.0087pK1.8 − 0.0103 − 0.0013

where, p−
corrK1.8 is the corrected momentum for the negative pion beam in a unit ofGeV/c. In the case of 1.2 GeV/c beam momentum used in the 6 Li(π − , K + ) reaction,
the amount of correction is −1.2 MeV/c. Figure 3.22 shows momentum difference foreach beam momentum and correction fuction of the beam momentum. The systematicaluncertainty of the beam momentum is estimated to be ±1.32 MeV/c from the momentum
deviations in other beam-through runs at 0.8, 1.0, 1.2 GeV/c.
Table 3.4: momentum correction
run
pK1.8
pcorrK1.8(GeV/c)(GeV/c)Beam Through 0.90001±0.0004 0.89758±0.0004
1.37710±0.0005 1.37884±0.0004
Σ+Σ−
1.38220±0.0005 1.38262±0.0005

dp(MeV/c)-2.43±0.06+1.74±0.12+0.44±0.11

Momentum Difference [MeV/ c]

3.6. MOMENTUM CORRECTION

65

4
3
2
1
0
-1
-2

0.8

0.9

1

1.1

1.2
1.3
1.4
Momentum[GeV/c]

Figure 3.22: Momentum difference measured with the K1.8 beam line and the SKS.
Fulled circles represent beam through runs at beam momenta of 0.8, 0.9, 1.0 and 1.2
GeV/c. Open circle represents momentum difference of the Σ+ production run, whereexpected beam momentum is estimated with the mass difference from PDG value of Σ+ .

Chapter 4
Experimental results
4.1

Good (π −, K +) events

Good (π, K) events are selected as shown in an analysis flow chart in Fig. 4.1. In
hodoscope analysis, the number of hits of BH2 within 2 ns of the time window is required
to be only one hit, and the number of hits of TOF is required to be one hit as well within
100 ns of time window. Furthermore, large ADC value of TOF is rejected as proton
like events. In BFT analysis, hit clusters of BFT are selected within 6 ns of the time
window. The number of clusters are not limited at this time. In BC3 and BC4 tracking,χ2 was required to be less than 30. Hit consistency of hit position between the track
and the BH2 hit segment was checked. After the selection, we carry out the K1.8
tracking and reconstruct the beam momentum. The number of K1.8 track candidates
were NBF T × NBC34tracks . As shown in Fig. 3.10, K1.8 tracks were selected with BFT
XU and YV correlation cuts. After this cut, the number of K1.8 tracks is required to beone.
In SFT-SDC2 and SDC3-SDC4 tracking, χ2 was required to be less than 30 and 20,
respectively. If these are satisfied, SKS tracking is carried out by using a Runge-Kutta
method. χ2 of SKS tracks are selected to be less than 10. Scattered kaons are selected
within the mass squared resolution of ±2σ. After this selection, the number of SKS
tracks is required to be one. In order to suppress accidental K1.8 tracks, the vertex
analysis including the SSD is performed. To increase the S/N ratios, the number ofhits of SSD selected to be one. After corrected the K1.8 track by SSD, vertex position is
calculated. Good (π, K) reaction events were selected in the criteria that closest distanceis less than 5 mm and vertex position is within the real size +20 mm in the z-direction
and real size in the x- and y-directions. The efficiency of each analysis procedure is
described in Chap 4.2.

66

4.1. GOOD (π − , K + ) EVENTS

67

New Event

BFT

BC3&4

Hodoscope

SFT&SDC2

SDC3&4

Analysis

Tracking

Analysis

Tracking

Tracking

χ2<30

χ2<20

χ2<30

|BFT time|<3ns|BH2 time|<1ns
TOF ADC Cut

K1.8

SKS

Tracking

Tracking
χ2<10NTrack=1

NTrack=1

Beam πPID:Mass Square<2σ

Scattered K
SSD Analysis
SSD NHit=1
Vertex reconstructclosest distance<5 mmgood vertex point
Good PIK event

Figure 4.1: Flow chart of the offline analysis. The order of the analysis is shown in each
box.

68

4.2

CHAPTER 4. EXPERIMENTAL RESULTS

Cross Section

The cross section was obtained from the experimental yield NK of the good (π − , K + )events as
 
NK
1
1
A
dσ
·
·
,
·
=
dΩ
(ρx)·NAvo (Nbeam ·fbeam ·ǫK1.8 ) ǫSKS ·∆Ω (ǫπK · ǫdaq )ǫK1.8 = ǫBF T · ǫBC3·4 · ǫK1.8track ,ǫSKS = ǫT OF · ǫLC ·fAC · ǫSF T ·SDC2 · ǫSDC3·4 · ǫSKStrack · ǫP ID ·fdecay ·fabs ,ǫπK = ǫSSD · ǫcloseDist · ǫsingle−πK · ǫvertex ,where A is the target mass number (A=6 in 6 Li, A=7 in proton in the (CH2 )n and A=12
in graphite), ρx is the target thickness in g/cm2 , NAvo is the Avogadro’s number, NBeam
is the number of the total beam particles measured as the scaler counts of the sum of each
BH2 segments. ∆Ω is the effective solid angle of the SKS. ǫ’s and f ’s are the experimental
efficiency factors. The factors represent the detector and analysis efficiencies, the dataacquisition efficiency, the muon contamination effects in the beam, the K decay effects,
and the K absorption effects, where symbols are defined in Table 4.1. The precision of
Table 4.1: The list of the experimental efficiency factors.
Factors
Meaning
Values (%)ǫdaqData-acquisition efficiency
77.6±0.8
ǫBF T
BFT efficiency
97.6±0.2
ǫSF T ·SDC2 SFT·SDC2 tracking efficiency 92.0±0.6
BC3·4 tracking efficiency
99.4±0.1
ǫBC3·4
ǫK1.8track
K1.8 tracking efficiency
96.4±0.3
ǫT OF
TOF efficiency
99.9±0.1
ǫLC
LC efficiency
97.8±0.3
fLAC
LAC accidental veto factor
88.0±1.5
SDC3·4 tracking efficiency
98.4±0.2
ǫSDC3·4ǫSKStrack
SKS tracking efficiency
90.2±0.3
ǫSSDSSD efficiency
96.1±0.5
ǫP ID
PID efficiency in SKS
95.4±0.2
ǫsingle−πK single track ratio
52.1±1.2
closest distance cut efficiency
97.1±0.2
ǫcloseDist+fabs
K absorption factor
95.6±0.5ǫvertex
Event vertex cut efficiency
94.8±0.5
the cross section is determined by those of ρx, ∆Ω and efficiency factors. The acceptanceof the SKS was calculated with a Monte Carlo simulation. Each efficiency factor was
estimated with various calibration data or Monte Carlo simulations. In this section, we
discuss how they were obtained, and finally we estimate the total systematic error of thecross section.

4.2. CROSS SECTION

4.2.1

69

Efficiency

Several efficiencies and correction factors are mainly the averaged values during the6Li(π − , K + ) production runs. The error is determined from the root mean squares ofthe efficiency fluctuation of all runs.
Data acquisition efficiency
The data acquisition efficiency (ǫDAQ ), caused by the dead time of the data acquisition
system, was obtained as a ratio of the number of events 1st-level trigger accepted by
the data acquisition system to that of the generated triggers. ǫDAQ was obtained as afunction of the trigger rate, and a typical value of ǫDAQ was 77.6±0.8% at a trigger rateof about 2200/2.0 sec per spill. The large error comes from difference of the intensity inDecember 2012 (12 MHz/spill) and January 2013 (14 MHz/spill).
Beam normalization factor
The beam normalization factor (fbeam ) represents the fraction of pions in Nbeam . Nbeam
includes electrons and muons because the scaler of BH2 did not require the GC veto.
The fraction of electron contamination (fe )is estimated from the coincidence of GC andBH2. At the high intensity beam, GC signal was saturated at more than 1 MHz due
to only one phototube equipped with GC. Electron contamination was evaluated with athe low intensity primary proton beam with the same slit condition as in the production
runs because the electron contamination also depends on the slit condition. As a result,the electron contamination of the beam was found to be 10%. The contamination ofmuons is caused from two sources, those delivered from the upstream of the mass slit
and those from the π → µ decay between the mass slit (MS2) and BH2.
The muons coming from upstream of MS2 is simulated with Decay TURTLE code [59],and estimated to be 0.5%. The Decay TURTLE takes care of the properties of beam,such as the beam profile and the number of beam particles, at each beam line component. For the Decay TURTLE calculation, the profile of the incident beam generated
from the T1 target and the properties of the beam line components were parametrized as
the input file. For example, the properties of a dipole magnet, such as the aperture, theeffective length of the central track, the field strength and gradient, were the inputs. The
particle trajectories were simulated with the transfer matrix constructed by the input
parameters of the beam line magnets, while in the electrostatic separators, the trajectories were calculated by using the Runge-Kutta calculation method. The trajectories
which stopped at the several slits or went out side of the magnet aperture were rejected.
The muons coming from the π → µ decay between MS2 and BH2 were estimatedfrom y-direction distribution at BFT. In the K1.8 tracking, after calculating the δ value,y, dx/dz and dy/dz at BFT are obtained from δ. When the y and dy/dz distribution isout of the BFT effective area, we treat it as from the decay muon. Therefore, this factor
includes K1.8 tracking efficiency.
In total, the value of fbeam ≡ (1 − fµ )(1 − fe ) was estimated to be 89.5 ± 5.0%. The
reason of the large error is caused the electron contamination factor, fe . In the present
data, according to the primary beam intensity, the ratio of the electron contamination

70

CHAPTER 4. EXPERIMENTAL RESULTS

varied in spite of slit is fixed. In principle, the ratio should be constant even if the
primary beam intensity change. Since we don’t understand this phenomena completely,
we put this change systematic error.
BFT efficiency
In order to obtain the BFT efficiency, we used the BEAM trigger events mixed in the(π, K) data. The BFT efficiency was defined asǫBF T =N (HitBF T ×πBeam),
N (πBeam)

where N (πBeam) is the number of events of the BH2 trigger data, and N (HitBF T ×
πBeam) the number of good BFT hits found in the proper BEAM trigger data. The
good BFT hits is selected by the ±3 ns time window. The efficiency is an average value
during the 6Λ H production runs.
BC3-BC4 tracking efficiency
The BC3-BC4 tracking efficiency is defined asǫBC3·4 =N (T rackBcOut ×πBeam).
N (πBeam)

It was the total efficiency including the detection efficiency and the analysis efficiency tofind a good straight track. Due to very high intensity beam, we applied “BH2 Filter”
method which put a limitation on the hit candidate search area by using BH2 hit segment
information. The BC3-BC4 efficiency is estimated to be 99.4±0.1%.
SSD efficiency
The SSD efficiency is defined asǫSSD =N (HitSSD × T rackBcOut × BEAM ).
N (T rackBcOut × BEAM )The N (T rackBcOut × BEAM ) requires the extrapolated hit position at SSD estimatedfrom the BC3-BC4 track is in the effective area of SSD. The SSD efficiency is estimatedto be 96.1 ± 0.5%.

4.2. CROSS SECTION

71

K1.8 tracking efficiency
The K1.8 tracking efficiency (ǫK1.8track ) was the analysis efficiency to reconstruct a particle trajectory in the beam spectrometer defined asǫK1.8track =N (K18track×BF T Hit = 1×BC3·4track = 1)
N (BF T Hit = 1×BC3·4track = 1)

where N (BF T Hit = 1×BC3·4track = 1) was the number of single good track foundin the BFT time cut (|time| <3 ns) and BC3 and BC4 local tracking (χ2 <30), andN (K18track × BF T Hit = 1 × BC3·4track = 1) is the number of good K1.8 track foundin the single good tracks of both BFT Hit and BC3 and BC4 local tracking requiring
the xu and yv cut in Fig 3.10. It was found to be 96.4±0.3%. This value includes the
decay muon comes from downstream of the MS2.
TOF and LC efficiency
The detection efficiency of TOF and LC was estimated from the beam-through run with
BEAM trigger. The TOF and LC efficiency was obtained as
N (T OF Hits×SdcOutT rack > 0×LCHits > 0×AcHits),
N (SdcOutT rack > 0×LCHits > 0×AcHits)
N (LCHits×SdcOutT rack > 0×T OF Hits > 0×AcHits)=,
N (SdcOutT rack > 0×T OF Hits > 0×AcHits)ǫT OF =
ǫLC

where N (SdcOutT rack > 0 × T OF Hits > 0 × AcHits) is the number of π tracks
which should pass through the effective area of TOF selected by the TDC informationof LAC and LC, and N (T OF Hits × SdcOutT rack > 0 × LCHits > 0 × AcHits) isthe number of those π tracks detected by TOF. LC is the same situation as TOF. The
momentum range of π is in 0.8 – 1.0 GeV/c. The efficiency of TOF and LC are foundto be ǫT OF = 99.9 ± 0.1% and ǫLC = 97.1 ± 0.2%, respectively. In LC efficiency, theµ events from the pion decay after passing through TOF was included in the efficiency.
The efficiency was assumed to be the same for K because the light yield of Čerenkov
photons by K in the momentum range from 0.8 to 1.0 GeV/c was high enough than thediscriminator threshold.
Accidental veto factor of LAC
The accidental veto factor of LAC was estimated from the special (π, π) trigger data inwhich the information of LAC was not required. For the estimation, we used scatteredproton events which should not be detected by LAC. The LAC accidental veto factor
was obtained fromN (AC×P roton)
fAC = 1 −,N (P roton)
where N (P roton) is the number proton track which should pass through the effective
area of LAC. Figure 4.2 shows the TDC spectrum of proton event in the (π, K) trigger.
We estimated the efficiencies with the three cut criteria, loose cut (40 ns), normal cut(30 ns) and tight cut (20 ns).

72

CHAPTER 4. EXPERIMENTAL RESULTS

12
10
8
6
4
2
0

-20

0

20

40

60

80
100
Time LAC

Figure 4.2: Time distribution of LAC in proton event in the (π, K) trigger.
SFT and SDC2 tracking efficiency
The efficiency of SFT and SDC2 tracking (ǫSF T ·SDC2 ) is the total efficiency including thedetector efficiency and the analysis efficiency to find straight tracks at the entrance of
the SKS magnet. It was estimated by the same way as that of BC3 and BC4 by using
the BEAM trigger events mixed in the (π, K) data. It was found to be 92.0±0.6%.
Since the efficiency is not affected for a small energy-loss difference between pion andkaon, we assumed the efficiency is the same for K. The SFT and SDC2 local tracking
efficiency is the average value during the 6Λ H production run.
SDC3 and SDC4 efficiency
The efficiency of SDC3 and SDC4 (ǫSDC3·4 ) is the total efficiency including the detector
efficiency and the analysis efficiency to find straight tracks at the exit of the SKS magnet.
We estimated the efficiency using scattered proton events recorded in the PIK trigger
data (the (π, p)X events) in which the particle does not decay in flight. Figure 4.3
shows the scatter plot between the horizontal scattering angle measured by SFT and
SDC2 local tracking and the flight time between BH2 and TOF. The proton events wereselected as shown in the figure. The SDC3 and SDC4 efficiency was estimated from thenumber of those selected proton events (N (P roton)) asǫSDC3·4 =N (SDC3·4T rack × P roton),
N (P roton)

where N (SDC3·4T rack × P roton) was the number of good tracks of these proton events
found in the SDC3 and SDC4 (χ2 < 20) local tracking. It was found to be 98.4±0.2%
which was the average of typical runs whose event number was statistically large enough4.2. CROSS SECTION

73

Time-of-flight (BH2-TOF) [ns]during the Σ production run. The error was determined from the root mean squares ofthe efficiency fluctuation for each run.
32
30

p

28
26

K

24
22

π

20
18
-0.4

-0.3

-0.2

-0.1

0
0.1
0.2
0.3
0.4
Horizontal scattering angle (dx/dz) [rad]Figure 4.3: The The correlation of time-of-flight and scattering angle (dx/dz).

SKS tracking efficiency
The SKS tracking efficiency ǫSKStrack was estimated by using the (π, p)X events recordedin the PIK trigger because the proton does not decay in flight. It is obtained asǫSKStrack =N (SKST rack × SdcInT rack = 1 × SdcOutT rack = 1 × P roton),
N (SdcInT rack = 1 × SdcOutT rack = 1 × P roton)

where N (SdcInT rack = 1 × SdcOutT rack = 1 × P roton) was the number of single goodtracks of proton events found in the SFT and SDC2 (χ2 < 30) and SDC3 and SDC4
(χ2 < 30) local tracking, and N (SKST rack × SdcInT rack = 1 × SdcOutT rack =1 × P roton) is the number of good SKS track found in the single good tracks of both
SFT-SDC2 and SDC3-SDC4 local tracking.
Figure 4.4 shows the efficiency as a function of the scattering angle. The SKS tracking
efficiency for each angle (θsks ) was estimated as a ratio of the number of events accepted
as a good trajectory within the selected scattering angle region by the tracking analysis tothe number of events which have good straight tracks within the selected scattering angle
calculated by SFT·SDC2 trajectory (θSF T ·SDC2 ). The scattering angle (θSF T ·SDC2 ) was
calculated by using the horizontal and vertical angles measured by SFT·SDC2 tracking.
Good straight tracks at both of the entrance and exit of SKS were also required. The
efficiency for the scattering angle larger than 17 degrees was rapidly worse because themagnetic field was not reproduced well in the fringing field region, namely the region
near the pole edge and the coil of the SKS magnet.
Figure 4.5 shows the missing mass resolution of Σ− as a function of the χ2SKS . It was
found that the events whose the χ2SKS is less than 10 kept the missing mass resolution

74

CHAPTER 4. EXPERIMENTAL RESULTS

efficiencyof less than 2.5 MeV/c2 (FWHM). We took into account of tight cut to χ2SKS < 10 tokeep good missing mass resolution.

1
0.95
0.9
0.85
0.8
0.75
0

2

4

6

8

10 12 14 16 18 20 22
Scattering Angle[degree]

Figure 4.4: The SKS tracking efficiency as a function of the scattering angle.

75

6
5
4
3
2
1

-

Σ Resolution (FWHM) (MeV/c2)

4.2. CROSS SECTION

0
0

10

20

30

40
50
χ2 of SKS tracking

Figure 4.5: The missing-mass resolution of Σ− as a function of the χ2sks
Scattered particle identification efficiency
As shown in Fig. 3.14, mass squared is calculated by β and momentum of scatteredparticles. To select the scattered kaons, we applied the momentum dependent cut forthe mass squared because the mass squared resolution depends on the momentum.
As shown in Fig. 3.15, the correlation of the mass squared and the momentum after
selecting the χ2sks < 10. We selected kaons by a momentum dependent cut at ±2σ ofthe mass squared resolution as indicated with curves in the figure. The contaminationof protons in the K + cut region is less than 1% below the particle momentum of 1.1
GeV/c. The efficiency of particle identification was 93.8±0.2%.
Single PIK track efficiency
The number of PIK track is defined as
N (P IKtrack) = N (K1.8track) × N (SKStrack) × N (SSDHit).
Therfore, single PIK track is defined as,ǫsingle−πk =N (P IKtrack = 1)
N (P IKtrack > 0)

Figure 4.6 shows the number of PIK tracks. The single PIK track efficiency is estimatedto be 52.1±1.2%. The reason of lower efficiency is mainly due to high multiplicity in
SSD. The single hit(track) ratio of K1.8 track, SKS track and SSD hit were 85.1%, 92.1%
and 66.5%, respectively. Most of the high multiplicity hits of SSD were due to accidental
hits

76

CHAPTER 4. EXPERIMENTAL RESULTSCounts

90000
80000
70000
60000
50000
40000
30000
20000
10000
0
0

1

2

3

4

5

6
7
8
9 10
# of PiK track events

Figure 4.6: The number of PIK tracks candidates.

Vertex cut efficiency
As mentioned in Sec. 3.4, the vertex cut was applied to select good (π, K) events fromthe target region. The vertex resolution for very forward scattering angle events wasworse than the other angular events as shown in Fig. 3.17. Therefore, we estimated thevertex efficiency as a function of scattering angle. A vertex cut region in the z-direction
was selected a wider vertex region than the real target size +20 mm and in the x- andy-direction was selected real target size. Figure 4.7 shows the vertex efficiency with eachsteps of scattering angle. The efficiency (ǫvertex ) was lower at the small angles, and was
obtained to be 94.8±0.5% in average for 2◦ –14◦ . Figure 4.8 shows a scatter plot between
the scattering angle and z-vertex distribution. As shown in the figure, the reconstructionof the z-vertex for very forward scattering angles failed because of difficulty to obtainthe closest distance between forward track of the beam pion and the scattered kaon. For
the scattering angle less than 2◦ , in particular the z-vertex resolution was too bad toeliminate the contribution of SSD.

K decay factor
Since the βγcτ of kaon around the momentum of 0.8–0.9 GeV/c is 6.0–6.8 m, a part of thekaons produced in the target decay before they reach the SKS downstream detectors. The
survival rate in the SKS track reconstruction process was estimated from the production
data event by event. The flight path length from the target to LAC was 4.6 m in average.
From this value, averaged K decay factor is estimated to be 43.7±0.7%.

efficiency [%]4.2. CROSS SECTION

77

100
95
90
85
80
75
70
65
60

2

4

6

8

10
12
14
16
Scattering angle [degree]

Vertex Z [mm]Figure 4.7: Vertex reconstruction efficiency as a function of the scattering angle.

200
150
100
50
0
-50
-100
-150
-200
0

2

4

6

8

10

12
14
16
18
20
Scattering angle [degree]

Figure 4.8: Scatter plot between the scattering angle and z-vertex distribution for the(π − , K + ) data.

78

CHAPTER 4. EXPERIMENTAL RESULTS

K absorption factor
Some of the kaons produced in the target would interact with materials in the spectrometers along the flight path. The K + N inelastic cross section around 0.85 GeV/c is about
2.0 mb. The absorption rate (fabs ) was estimated by a simulation, in which the target,
the counters, the drift chamber gas and windows, the helium bags and air between thedetectors were considered as materials in the spectrometer as shown in Table 4.2. Alongthe path of the scattered kaons, the TOF (3.10 g/cm2 ) and LAC (2.26 g/cm2 ) was dominant, while the total material thickness was about 10 g/cm2 . We took into accountboth inelastic and elastic interactions in the simulation. The K events were generated at
the target with a uniform momentum distribution (0.75–0.95 GeV/c), a uniform angular
distribution (θ < 20◦ ) and a reaction rate (fabs ) of the kaon was estimated as
fabs = 1 −NKhitonLC.
NKgenerated

The rate was estimated to be 4.4±0.3%. The error was estimated by the difference ofthe material thickness along the particle trajectories.
Table 4.2: Typical materials in the spectrometers along the flight path.
Material
Thickness (g/cm2 )Target
3.50
TOF
3.10
LAC
2.26
0.54
AC frame (Al)

4.3. ACCEPTANCE OF SKS

4.3

79

Acceptance of SKS

The effective solid angle of the SKS (∆Ω) was calculated with a simulation. For a fixedinterval of the scattering angle of ∆θ, the effective solid angle was calculated as a functionof scattering angle θ and momentum p. In the event generation, the distribution of thebeam profile defined as a function of (xb , yb , ub , vb ) was produced from the experimental
data, where xb , yb , ub and vb are the horizontal and vertical positions and their derivativesof a beam particle at the target. The scattered kaons were generated uniformly inpolar angle θ (cos(θ − 21 ∆θ) < cos θ < cos(θ + 21 ∆θ)), uniformly in azimuthal angle φ(0 < φ < 2π) and uniformly momentum p (p − 12 ∆p < p < p + 21 ∆p).
In the simulation, the combination of the TOF and LC counters used in the matrix
trigger was also taken into account. In the present analysis, we selected events in the
scattering angle from 2◦ to 14◦ . Therefore, the effective solid angle was calculated for2◦ < θ < 14◦ .
Figure 4.9 shows the acceptance of SKS in the 2.2 T mode. It includes the matrix of
TOF and LC combinations. The acceptance is represented by the arbitrary unit (numberof triggered event in the simulation).
The momentum region of the scattered particle of 0.85–0.90 GeV/c corresponds tothe bound region of the 6Λ H hypernucleus, and less than 0.85 GeV/c corresponds to thecontinuum region of the Λ and Σ state. The momentum corresponds to bound region of6
Λ H is well covered by the SKS spectrometer.

CHAPTER 4. EXPERIMENTAL RESULTS

Momentum [GeV/c]

80

1.5
1.4

(a)

1.3
1.2
1.1
1
0.9
0.8
0.7

Solid angle[msr/deg]

0.6
0

8

2

4

6

8

10 12 14 16 18 20
Scattering angle [degree]

PK = 800-900 MeV/c

(b)

7
6
5
4
3
2
1
0

2

4

6

8

10 12 14 16 18 20
Scattering angle [degree]

Figure 4.9: The acceptance of SKS in the 2.2 T mode. It shows the total acceptancewith TOF and LC matrix combination trigger selection. (a) : The scattering angle
vs momentum plot. The acceptance is represented by the arbitrary unit (number oftriggered event in the simulation.). (b) : Solid angle per deg in the region of pK =800–
900 MeV/c as a function of scattering angle.

Integrated acceptance [msr]4.4. MISSING-MASS SPECTRUM OF THE 6 LI(π − , K + ) REACTION

120

81

6
ΛH

100
80
60
40
20
0

0.6

0.8

1

1.2
1.4
Momentum [GeV/c]

Figure 4.10: The integrated acceptance from 2◦ to 14◦

4.4

Missing-mass spectrum of the 6Li(π −, K +) reaction

As mentioned in Sec.3.1, missing mass was obtained from this expression.
q
M = (Eπ + MA − EK )2 − (p2π + p2K − 2pπ pK cos θπK ),pπ and pk were used corrected value which is described in Sec.3.6.4 and Sec.3.6.2. Eπ
and EK were used energy loss corrected value at the target with Bethe-Bloch formula.
The double differential cross section is defined as
d2 σ
A
nK
=
·
,
dΩdM
NA · ρx Nbeam · ∆Ω · ∆M · ǫ(4.1)

where nK is the number of detected kaons in the missing-mass interval ∆M. ǫ is the over
all experimental efficiency described in Sec.4.2. Where, ǫskstrack and ǫvertex are correctedwith event by event in each θ. ∆Ω is also scaled with SKS acceptance in each θ. The
other values are constant of all runs.
Figure 4.11 (a) shows the missing-mass spectrum of the 6 Li(π − , K + ) reaction at the
momentum of 1.2 GeV/c in the experimental counts per 1 MeV/c2 . Figure 4.11 (b) shows
the missing-mass spectrum of the double differential cross section of the laboratory frame,
d2 σ lab /dΩ/dM in a unit of nb/sr/(MeV/c2 ). Both spectra are selected the scattering
angle from 2◦ to 14◦ in the laboratory frame because the estimation of the spectrometer
acceptance has small ambiguity in the angular range. The uncertainty of the missing

82

CHAPTER 4. EXPERIMENTAL RESULTS

mass scale is ±1.26 MeV/c2 which is estimated from the beam momentum uncertainty±1.34 MeV/c. The continuum of the unbound Λ formation reaction and the componentof the Σ− quasi-free production reaction are observed in the missing-mass range of 5810–
5880 MeV/c2 and above 5880 MeV/c2 , respectively. A magnified view in the missingmass range of 5795–5830 MeV/c2 is shown in the inset. Around the 4Λ H+2n particle
decay threshold indicated by the arrow (5801.7 MeV/c2 ), no significant peak structure
is observed.

4.4. MISSING-MASS SPECTRUM OF THE 6 LI(π − , K + ) REACTION

350

Counts/(MeV/c2)

300
250
200

Counts/(MeV/ c 2)

(a)

83

10
8
6
4
2
0

150

4
ΛH+2n

5800
5810
5820
5830
Missing Mass [MeV/c 2]

100
50
0

50
40
30
20
10
0

d 2σlab/d Ω/d M [nb/sr/(MeV/c 2)]

d 2σlab/d Ω/d M [nb/sr/(MeV/ c2)](b) 60

5800
5850
5900
2
Missing Mass [MeV/c ]
4
3
2

4
ΛH+2n

1
0

5800
5810
5820
5830
Missing Mass [MeV/c 2]

θ lab = 2°-14°
5800
5850
5900
Missing Mass [MeV/c2]

Figure 4.11: (a) The missing-mass acceptance uncorrected spectrum of the 6 Li(π − , K + )reaction at the momentum of 1.2 GeV/c. (b) The missing-mass acceptance corrected
spectrum.

Chapter 5
Discussions
5.1

Analysis of 12ΛC

In order to evaluate the missing-mass resolution in a kinematical condition close tothat of the 6 Li(π − , K + )6Λ H reaction, we measured the 12 C(π + , K + )12Λ C reaction at the
momentum of 1.2 GeV/c. A graphite target of 3.6 g/cm2 in thickness was used, andthe beam intensity was 4.1 × 106 pions/spill. Figure 5.1 shows the excitation energy
spectrum of the 12Λ C hypernucleus obtained from the measurement. Although it is not
acceptance corrected, the acceptance is almost flat in the excitation energy between -5
MeV and 10 MeV. The ground (sΛ ) and excited (pΛ ) states were clearly observed. The
ground state region was fitted with three Gaussian distributions corresponding to theground and to known excited states at 2.833 MeV and 6.050 MeV [62]. A same widthof the Gaussian function is used for the three states. The missing-mass resolution isestimated to be 3.23 ± 0.02 MeV in FWHM for the 6 Li(π − , K + )6Λ H.

84

5.1. ANALYSIS OF 12Λ C

85

140

p

Counts/0.5MeV

120
100

Λ

sΛ

80
60
40
20
0
-20 -15 -10 -5 0 5 10 15 20 25 30
Excitation Energy [MeV]

Figure 5.1: Excitation energy spectrum of the 12 C(π + , K + )12
Λ C reaction at the momentumof 1.2 GeV/c. The ground sΛ and excited pΛ states are clearly observed. The missing
mass resolution is estimated by fitting the ground and known excited states. The dashedcurves show the best fit Gaussian functions for these states and the solid curve is the
sum.

86

CHAPTER 5. DISCUSSIONS

Analysis of the Σ±

5.2

700
600

(a)

500
400
300

Counts/0.5MeV/c

Counts/0.5MeV/c

We measured the p(π − , K + )Σ− and the p(π + , K + )Σ+ reactions at 1.377 GeV/c to calibrate the beam momentum with a (CH2 )n target of 3.4 g/cm2 in thickness. The pion
beam momentum of 1.377 GeV/c was selected so that the produced K + momentum in thep(π ± , K + )Σ± reaction coincides with that in the 6 Li(π − , K + )6Λ H reaction at 1.2 GeV/c.
The beam intensities in the Σ− and Σ+ production runs were 1.3 × 107 and 3.5 × 106
pions/spill, respectively. Figure 5.2 shows the missing mass spectrum for Σ+ and Σ− .
The peaks of Σ+ and Σ− were clearly observed. The background around the peak of Σ+
was due to Λ quasi-free production from 12 C in (CH2 )n . Since there was no difference of
missing mass resolution between the Σ+ and Σ− production runs, 2.54 ± 0.03 MeV/c2
in FWHM for both measurements, it is concluded that the beam rate dependence of themass resolution is negligible. The differential cross section of the Σ− production reac400
350

250
200
150

200

100

100

50

0

(b)

300

1.16

1.18
1.2
1.22
Σ missing mass [GeV/c]
-

1.24

0

1.16

1.18
1.2
1.22
1.24
Σ missing mass [GeV/c]+

Figure 5.2: Missing-mass spectrum of Σ± .
tion is shown in Fig. 5.3 as a function of the scattering angle in the laboratory frame.
Figure. 5.4 shows the differential cross section of Σ+ production after subtracting the Λ
quasi-free events by linear fit. Figure 5.5 and Figure 5.6 shows the integrated differential
cross section, dσ/dΩcm , in the center of mass frame (full circle) in the angular range ofcos θcm =0.8–1.0 for the π − p → K + Σ− reaction. The cross section is compared with thecross sections previously reported by Good et al. [63] (open circles) and Dahl et al. [64](open box). The differential cross sections gradually decrease with the increase of theπ − beam momentum. It seems the present result is consistent with the general trend.
Figure 5.6 shows the cross section for the π + p → K + Σ+ reaction, which is also
compared with an old repoted data by Candlin et al. [65]. It increases gradually with
the increase of the π + beam momentum, and the present result is consistent with thegeneral trend. From these comparison, we estimate the systematic error of the present
cross section measurement is 10%.

Cross Section [µb/sr]

5.2. ANALYSIS OF THE Σ±

87

80
70
60
50
40
30
20
10
0

2

4

6

8
10
12
14
16
Scattering angle (lab) [degree]

Cross Section [µb/sr]

Figure 5.3: The differential cross section of the Σ− production as a function of thescattering angle.

500
400
300
200
100
0

2

4

6

8
10
12
14
16
Scattering angle (lab) [degree]

Figure 5.4: The differential cross section of Σ+ production as a function of the scattering
angle.

88

CHAPTER 5. DISCUSSIONS

π-p →K +Σ

30

dσcm/dΩ [µb/sr]

25-cosθ cm = 0.8 - 1.0

Good [28]Dahl [29]Present

20
15
10
5
0
1.1

1.2
1.3
1.4
1.5
Beam Momentum [GeV/ c]

Figure 5.5: The differential cross section of the Σ− production compared with old experiments as a function of the π − beam momentum.

π+p →K +Σ+60

dσcm/dΩ [µb/sr]

50cosθ cm = 0.8 - 1.0

40
30
20
10
0

CandlinPresent

1.3

1.35
1.4
1.45
Beam Momentum [GeV/ c]

1.5

Figure 5.6: The differential cross section of the Σ+ production compared with an old
experimental data as a function of the π + beam momentum.

5.3. BACKGROUND LEVEL

5.3

89

Background level

In order to estimate the statistical significance of a small peak structure in the hypernuclear mass spectra, we need to understand the background level in the spectrum. In
the present analysis, it was estimated with several procedures. The over bound region(5790–5802 MeV/c2 ) means the region where the binding energy is larger than that for
the ground state of a produced Λ hypernucleus. Accordingly, the yield in this regionmeans the background level if existed. Figure 5.7 shows a 6 Li(π − , K + ) spectrum in theover bound regions with three different cut parameter conditions in mass squared resolution, χ2sks and vertex. We found the main component of background comes from particle
miss-identification in the mass squared cut. As shown in Fig. 3.14, high intensity beamcauses different start timings after the true start timing. In that case, time-of-flight from
BH2 to TOF is faster than the true timing, which causes the particle miss-identification.
In the present analysis, background level in the region of 5700 to 5780 MeV/c2 wasestimated to be 0.39 ± 0.05 events per MeV/c2 .

CHAPTER 5. DISCUSSIONSCounts/(MeV/c2)

Counts/(MeV/c2)

Counts/(MeV/c2)

Counts/(MeV/c2)

90

7
6
5
4
3
2
1
0

(a) final spectrum

5760

5780
5800
Missing Mass [MeV/c2]

7
6
5
4
3
2
1
0

(b) 4σ cut of m2 resolution

7
6
5
4
3
2
1
0

(c) χ2 <50

7
6
5
4
3
2
1
0

(d) vertex cut = real size ±50mm

5760

5820

5780
5800
Missing Mass [MeV/c2]

5820

5780
5800
Missing Mass [MeV/c2]

5820

sks

5760

5760

5780
5800
Missing Mass [MeV/c2]

5820

Figure 5.7: Background level in the over bound regions of the 6 Li(π − , K + ) reaction in
the final analysis (a); (b)–(d) are the same histograms with loosened cut conditions inmass squared resolution, χ2sks and vertex cut

5.4. ESTIMATION OF UPPER LIMIT

5.4

91

Estimation of upper limit

As a first step of the calculation of an upper limit of the differential cross section,dσ lab /dΩ, for a state of 6Λ H, we estimated the number of observed events in the missingmass region around the 4Λ H+2n threshold. For the estimation of the number of events
associated to the production of a state, we set a missing-mass window of ±2σ, 5.44
MeV/c2 , in the missing-mass region. There were 3 events in the threshold region within
the missing-mass window. Therefore, we interpret the 3 events as observed events which
include background and possible signal events.
Another necessary information for the upper limit estimation is the number of background events. Population of events are observed in the missing-mass region lower than5780 MeV/c2 where we do not expect any physical backgrounds. The level of the event
population is 0.39 ± 0.05 events per 1 MeV/c2 in average. These events are instrumental
background due to particle miss-identifications. We assumed a similar level of backgrounds at the 4Λ H+2n threshold. The number of background events was estimated bymultiplying the average background level with the width of the missing-mass window.
If Poisson statistics is applied, the upper limit of the number of signal events is
estimated to be 4.80 at 90 % confidence level. Although we assumed a flat distributionof the background events, the missing-mass dependence of the background level is notobserved well due to the low statistics. Therefore, we employ another upper limit of 6.68
events coming from the background free hypothesis as a conservative estimation.
As shown in Fig 4.11, the differential cross sections are roughly 0.1 nb/sr for 1 eventfor the observed 3 events. However, the differential cross sections largely depend on
the observed scattering angles and may have a statistical bias. If an event happens tobe observed at the forward angle, the cross section is underestimated, and vice versa,
in our set up. To avoid the bias of the observation, we estimate the differential crosssection averaged over the selected angular range from 2◦ to 14◦ , and we obtain a valueof 0.18 nb/sr for 1 event. By using the value, the upper limit of the differential crosssection averaged in the scattering angle from 2◦ to 14◦ is estimated to be 1.2 nb/sr at
90% confidence level.

92

5.5

CHAPTER 5. DISCUSSIONSStructure of 6ΛH

In our 6 Li(π − , K + ) spectrum in Fig. 4.11, neither significant peak structure nor a large
yield is observed around the 4Λ H+2n particle decay threshold in the 6 Li(π − , K + ) reaction.
The 6Λ H hypernucleus is believed to have the 4Λ H+2n structure dominantly and have the0+ ground and the 1+ excited states which are analogous to the 0+ and 1+ spin-doubletsin 4Λ H. Our reaction should favor the 1+ state direct population at foward angles, because
the dominant spin non-flip amplitude of the (π − , K + ) reaction would not change thespin of 6Λ H with the same spin of 6 Li. We summarized three kinds of scenarios about6
Λ H structure as shown in Fig 5.8. As far as the FINUDA result is concerned [66], theobserved 6Λ H candidate events were interpreted as the primary population of the excited−
1+ state by the (Kstopped, π + ) reaction followed by the γ-ray transition to the ground0+ state because the direct population of the 0+ state should be suppressed due to the−small spin-flip amplitude in the (Kstopped, π + ) reaction. The FINUDA results indicate+that the excited 1 state, whose excitation energy is considered to be about 1 MeV,
should be particle bound, otherwise the γ-ray transition to the 0+ ground state shouldbe impossible. If the 1+ state was bound and the production cross section was comparablewith that for 10
Λ Li of 11.3 nb/sr, more than 60 events should be observed as a peak in theΛ bound region in the missing-mass spectrum of the 6 Li(π − , K + ) reaction. Therefore,
our observation is in conflict with the simple interpretation of the FINUDA observation.
Hiyama et al. [41] suggested that both 0+ and 1+ states are unbound. If it is the case,production cross sections may be smaller than the sensitivity of our measurement due tothe broad wave-functions of the unbound states which should have a small overlap withthe wave-function in the initial 6 Li nucleus.
Gal and Millener [40] discussed another possible interpretation of the FINUDA observation. They suggested a possibility of an unbound 1+ state, whose particle decay
width is extremely small and comparable with that of the M 1 γ decay to the ground0+ state due to kinematical and dynamical suppression of the emission of two neutrons
from the 1+ excited state.
The FINUDA collaboration also discussed another scenario for the spectrum of 6Λ H in
which two out of the three candidate events came from the population of the spin-triplet
states, 1+ , 2+ and 3+ , at around 3 MeV excitation [66]. Therefore, it is interesting
to compare our upper limit, 1.2 nb/sr, with quantitative theoretical estimations of the
production cross sections because the cross sections are sensitive to the binding energies
and the wave-functions of the low-lying states.
Scenario-1

Scenario-2

Scenario-3

6+

particle decay threshold
4
Λ

H+2n

+

1
+
0

+

~1 MeV

γ(M1)

1
+
0

FINUDA exp+

observe 1

1+0

possible

Λ

H
n

4
H
Λ

n

broaden+observation of 0

wave function

Figure 5.8: Level sturucture of 6Λ H with respect to the particle decay threshold of 4Λ H+2n.

Chapter 6
Conclusion
We have performed the measurement of 6 Li(π − , K + ) reaction at a beam momentum of 1.2
GeV/c and the missing-mass spectrum was obtained for the first time. To evaluate themissing-mass resolution of 6 Li(π − , K + ) reaction, we have also measured 12
Λ C prodcution
12++
with the C(π , K ) reaction. A clear peak structure was observed in the bound region,and the missing-mass resolution was estimated to be 3.23 ± 0.02 MeV/c2 . The Σ±
productions by the p(π ± , K + ) reactions were measured to calibrate the absolute massscale. For both Σ− and Σ+ produtions, the production cross section was consistent with
old experimental data. The momentum correction uncertainty was estimated to be 1.34
MeV/c which corresponds to 1.26 MeV/c2 in the absolute mass uncertainty.
In the missing-mass spectrum of the 6 Li(π − , K + ) reaction, no significant peak structure was observed around the 4Λ H+2n threshold. There were 3 events in the thresholdregion within the missing-mass window. Therefore, we interpret the 3 events as observed
events which include background and possible signal events. The background level was
estimated to be 0.39 ± 0.05 events per 1 MeV/c2 by evaluating the unphysical missingmass region in the missing mass of 5700–5780 MeV/c2 . When the Poisson statistics isapplied, we obtained the upper limit of 4.80 events at the 90% confidence level, and 6.68
events in the case of background free assumption.
The differential cross section per event was 0.18 ± 0.02 nb/sr under the average overthe selected angular range from 2◦ to 14◦ . Therefore the upper limit of the differential
cross section in the scattering angle from 2◦ to 14◦ is estimated to be 1.2 nb/sr at the
90% confidence level.
Our result did not favor a simple interpretation of the FINUDA observation thatboth 0+ and 1+ states of 6Λ H are bound. It suggests that reconsideration of the structureof the 6Λ H hypernucleus as well as 5 H would be needed. It is a key to fully understandwhether the 1+ excited state is bound or not.

93

Acknowledgements
First of all, I would like to acknowledge the J-PARC E10 collaborators and every person
I had a fortune to work with. If there were not for their contribution and advices, I
would have never been able to complete this work.
I would like to express my great thanks to Prof. Tomofumi Nagae, who has been mysupervisor at Kyoto University. He gave me a chance to research hypernuclei. He always
encouraged to me helpful suggestion about not only physics but also my life.
During my research at graduate school, I almost spent and worked at J-PARC. Especially, I belonged to Advance Science Research Center (ASRC) of Japan Atomic Energy
Agency (JAEA) during doctor course. I appliciate to Prof. Ken’ichi Imai, who has mysupervisor at ASRC. He always encouraged me with his warm advice and vivid sense forphysics when I had a trouble in the experiment and data analysis. I have also learned
from him about atitudes to the physical research as a physist.
I would like to express my great thank to Prof. Atsushi Sakaguchi, who is the
spokesperson of the J-PARC E10 experiment. When I was second degree of doctor
course, I expressed him that I want to write with a result of E10 experiment. He kindly
accepted my request, and made me the great part of J-PARC E10 experiment. I discussedwith him so many times about experimental preparetion and data analysis. Thanks tohim, I could get a good result of J-PARC E10 experiment.
I would like to thank to experimental preparation work together with Mr. S. Hayakawa,
Mr. R. Ota, Ms. M. Nakagawa and Mr. T. Soyama. I enjoyed and spent them. I could
not carry out the experiment without their great contributions. It was indeed a great
pleasure to work with them. For the construction of LAC, I would like to appliciate
to Mr. K. Matsuoka, Mr. T. Tanaka, Mr. K. Yoshida, who made a great effort theconstruction.
I would like to acknowledge the Dr. Kotaro Shirotori and Mr. Tomonori Takahashi.
They were pioneers of K1.8 beam line group. I have learned from them not only many
experimental techniques and analyses but also how to survive the J-PARC life.
I would like to greatly acknowledge the Hyperball group members. Prof. H. Tamura,
Prof. T. Koike, Dr. M. Ukai, Dr. K. Miwa suggested me the plan of experimental preparation work, and I learned the experimental techniques from them. I would appliciate
Mr. R. Honda, who worked together with me during preparation. He introduced somenew systems, Mass trigger, EASIROC, Fiber tracker. Were not for him, the experiment
would not succeed. I would like to thank Mr. T.O. Yamamoto, Mr. Y. Sasaki, Mr. Y.
Akazawa, Mr. K. Tanabe, Mr. Y. Yamamoto and Mr. T. Shiozaki for taking the E10experimental shift.
I have spent my graduate school days as a member of the ”Experimental Nuclear and94

95
Hadronic Physics Laboratory (NH)”. I wish to acknowledge the help and encouragement by Prof. Takahiro Kawabata, Prof. Megumi Naruki, Dr. Tetsuya Murakami, Dr.
Masayuki Niiyama and Dr. Hiroyuki Fujioka. I would like to express my great thanks
to Dr. A.O. Tokiyasu, Mr. M. Moritsu and Mr. Y. Ichikawa. I worked K1.8 beam line
construction with them. After the earthquake, two new members, Mr. S. Kanatsuki and
Mr. H. Ekawa participated in reconstruction of K1.8 beam line. They helped us andmade good efforts. For E10 experiments, Mr. N. Amano helped us to take a shift.
I have joined two experiment, J-PARC E19 and E27. I would address my thanks to
all the members of J-PARC E19 and E27 collaboration. I could not complete this thesis
work without their great effort.
The present experiment was made possible by the staffs of J-PARC and KEK. I would
like to express my great thanks to the Hadron beam channel group, accelerator groupand electronics group for their strong support for the experiment. Especially, I would liketo apliciate to Prof. Toshiyuki Takahashi and Prof. Masaharu Ieiri to plan the scheduleof beam time based on our request.
Finally, but not the least, I want to express my sincere gratitude to my parents,
Tsuneo Sugimura and Yachiyo Sugimura.

Appendix A
Missing-mass spectrum of the6Li(π −, K +) reaction
The missing-mass spectrum of the 6 Li(π − , K + ) reaction is shown in Fig.4.1 are presented
as table in Table A.1. The quoted values of M are the centers of the bins.
Table A.1:
The missing-mass spectrum of the6−+Li(π , K ) reaction as a table
M (MeV/c2 )5.78055.78155.78255.78355.78455.78555.78655.78755.78855.78955.79055.79155.79255.79355.79455.79555.79655.79755.79855.79955.80055.80155.8025

Cross section (nb/sr/(MeV/c2 ))0.261516
0.170215
0.589593
0.308068
0.342676
0.104584
0.197870
0.104559
0.108269
0.098477
96

error
0.261516
0.170215
0.589593
0.308068
0.342676
0.104584
0.197870
0.104559
0.108269
0.098477

97
M (MeV/c2 )5.80355.80455.80555.80655.80755.80855.80955.81055.81155.81255.81355.81455.81555.81655.81755.81855.81955.82055.82155.82255.82355.82455.82555.82655.82755.82855.82955.83055.83155.83255.83355.83455.83555.83655.83755.83855.83955.84055.84155.84255.84355.84455.84555.8465

Cross section (nb/sr/(MeV/c2 ))0.103825
0.179096
0.325925
0.449910
0.182671
0.395366
0.489352
0.396608
0.754853
0.533196
0.5901200.709881
1.02689
0.673250
1.07305
0.496787
2.32697
0.819468
2.330142.267432.680542.15475
1.422542.338932.30281
3.197362.44683
2.577902.77793
3.46666
2.84105
1.997162.160594.20301
3.573993.253843.97098
3.79696
5.655482.94090

error
0.103825
0.179096
0.188481
0.352849
0.182671
0.234316
0.312158
0.238876
0.436248
0.533196
0.488420
0.388345
0.454379
0.486807
0.437719
0.293376
0.744588
0.435082
0.828373
0.801049
0.949193
0.749864
0.586638
0.746463
0.736015
0.995696
0.8659020.777335
0.881818
0.931516
0.925927
0.5331710.739589
1.02601
0.864990
0.919864
1.03070
1.00140
1.320410.765158

98 APPENDIX A. MISSING-MASS SPECTRUM OF THE 6 LI(π − , K + ) REACTION
M (MeV/c2 )5.84755.84855.84955.85055.85155.85255.85355.85455.85555.85655.85755.85855.85955.86055.86155.86255.86355.86455.86555.86655.86755.86855.86955.87055.87155.87255.87355.87455.87555.87655.87755.87855.87955.88055.88155.88255.88355.88455.88555.88655.88755.88855.88955.8905

Cross section (nb/sr/(MeV/c2 ))2.62424
4.593025.44791
6.30463
4.97309
3.069082.60092
5.086814.92305
5.55673
5.42241
6.763614.709678.37088
7.931095.625115.98901
5.828495.75540
6.752135.80457
6.44626
7.63998
6.046366.29386
7.35880
7.66088
8.14266
10.84078.04116
10.71076.80287
11.79699.75552
12.8948
14.9469
11.08658.64651
15.0740
13.4330
14.7249
18.8072
16.0272
17.6510error
0.865682
1.26970
1.27135
1.45576
1.166590.820089
0.683837
1.24657
1.08983
1.15272
1.10359
1.46104
1.13872
1.66527
1.69320
1.14676
1.45607
1.175431.28771
1.39380
1.13888
1.56303
1.483101.37347
1.215631.36258
1.270171.30887
1.739481.44520
1.81752
1.48018
1.97306
1.59309
1.97793
2.12047
1.56808
1.28232
2.06657
2.086942.12751
2.40380
2.09475
2.51655

99
M (MeV/c2 )5.89155.89255.89355.89455.89555.89655.89755.89855.89955.90055.90155.90255.90355.90455.90555.90655.90755.90855.90955.91055.91155.91255.91355.91455.91555.91655.91755.91855.9195

Cross section (nb/sr/(MeV/c2 ))18.0245
17.7537
23.8277
22.317825.0563
22.9536
30.5418
34.241431.068436.2834
31.412235.006143.702140.6269
40.359437.8680
42.573437.9506
46.8424
51.4945
56.2153
60.5918
55.1737
56.873153.2186
59.757668.2275
54.2183
64.5318error
2.46906
2.203482.93337
2.567072.81378
2.36004
2.97880
3.463622.97440
3.455512.776433.286443.79665
3.43175
3.60800
2.968933.728172.942433.75536
3.92490
4.12532
4.26411
3.84419
4.172693.654153.90035
4.36938
4.243074.75118

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