KEK/J-PARC-PAC 2012-19

Charmed Baryon Spectroscopy via the (π, D∗− ) reaction
Y. Morino, T. Nakano,∗ H. Noumi† ,∗ K. Shirotori, Y. Sugaya, and T. Yamaga
Research Center for Nuclear Physics (RCNP), Osaka University,
10-1, Mihogaoka, Ibaraki, Osaka, 567-0047, JapanK. Ozawa‡
Institute of Particle and Nuclear Studies(IPNS),High Energy Accelerator Research Organization (KEK),
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
T. Ishikawa
Reserach Center for Electron Photon Science,
Tohoku University, 1-2-1, Mikamine,
Taihaku-ku, Sendai, Miyagi 982-0826, Japan
Y. Miyachi
Physics Department, Yamagata University, 1-4-12,
Kojirakawa-machi, Yamagata 990-8560, Japan
K. Tanida
Department of Physics and Astronomy,
Seoul National University, Seoul 151-747, Korea†

Spokesperson
Co-Spokesperson∗
alternative affiliation: IPNS, KEK, 1-1, Oho, Tsukuba, Ibaraki, 305-0801, Japan‡1

KEK/J-PARC-PAC 2012-19
December 10, 2012

Executive Summary
We propose the spectroscopic study of charmed baryons via the (π, D ∗− ) reactions at thehigh-momentum (high-p) beam line of J-PARC to investigate the diquark degree of freedom
in a hadron. The good diquark correlation is due to the color-spin interaction whose strengthis proportional to the inverse of a quark mass. Therefore, there would be only one gooddiquark pair in a charmed baryon, which makes the study of excited charmed baryons uniqueand interesting.
We will supplement the high-p beam line with the dispersive ion optical elements sothat a high-intensity pion beam with a resolution of ∆p/p=0.1 % can be delivered. A newlarge acceptance spectrometer for the D ∗− detection is designed to achieve a missing mass
resolution of ∼5 MeV. Charmed baryons from the ground state to highly excited statesof Ex ∼ 1 GeV will be identified in a missing mass spectrum of the p(π, D ∗− ) reaction.
In addition to the masses and widths of charmed baryons, the spectrometer enables us
to measure some of the decay branching ratios of an excited baryon by detecting decay
products.
Here, we propose new charmed baryon spectroscopy by means of the missing mass method
to shed lights on the diquark.

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I.

INTRODUCTION

Although we know the fundamental law of the strong interaction, quantum chromodynamics (QCD), the dynamics of hadrons at low energy is not easily described in terms of thebare quarks and gluons. As being strongly correlated systems, the construction of hadrons
may require good insight with more ingredients beyond the bare particles. The possible
formation of various kinds of active constituents at relevant energy scale as quasi-particles
is the origin of the variety of hadrons.
Due to the strong interaction effects, light u, d and s quarks are renormalized to emerge
as quasi-particles and become active building blocks of hadrons at low energy. Thus dressed
quarks are referred to as constituent quarks. Contrary, heavy charm and bottom quarks arealmost good constituents by themselves. The strongly renormalized u, d and s quarks andalmost bare c and b quarks are the basic building blocks of hadrons that we shall study. The
quark model based on these quarks have been generally successful especially for the groundstate hadrons [1]. It also describes an important feature of the nuclear force [2].
Yet, problems have been recognized among resonances. For instance; (1) not all quark
model states are observed, which is known as the missing resonance problem, and (2) many
resonances above decay channel threshold are not well described. The so-called exotic
hadrons are particularly so.
Diquarks have been discussed in hadron physics for a long time [7–10]. There are many
phenomenological suggestions or even ”evidence” of diquarks. The above-mentioned missing
resonance problem in baryons might be solved by introducing diquarks. Exotic hadrons
such as ”light-narrow” penta-quark state are explained as a positive parity state by diquark
picture, togather with the ”lightest” positive partity nucleon resonance, Roper [9]. Ref. [9]discusses also why the lightest scalar meson nonet appears below 1 GeV with a diquark
model.
The so-called good diquark is formed due to strong attraction in the color-spin (colormagnetic) interaction between two quarks (Appendix A). In baryonic system with lightquarks, the effect of the good diquark correlations may be difficult to see because 3 pairs of
diquark correlations are at equal weight. If a light quark is replaced by a heavy quark ina baryon, because the color-spin interection is proportional to the inverse of a quark mass
(Eq. A3), the other two light quarks are expected to correlate strongly, thus, may develope
a diquark. Lattice QCD calculations demonstrate strong spatial correlations between twolight quarks with a spin-singlet, color antitriplet configuration in a baryon with introducing
a static quark[11, 12]. A charm quark would act as a static quark and may isolate the othertwo light quarks. If the isolated two light quarks make a collective system, a relative motionin the light quarks (ρ mode) and a collective motion of them to the heavy quark (λ mode)
may split in excited states, as illustrated in Fig. 1. If this is the case, characteristic patternsof the level structure of excited states, such as Regge trajectories, might be seen. A diquark
mass may be determined from a slope parameter of a Regge trajectory. Although this is3

KEK/J-PARC-PAC 2012-19

FIG. 1: Schematic picture of quark correlations in a baryon. In a baryon with light quarks, thecorrelations are equal weight and the orbital excitation levels are degenerated, as illustrated in theleft hand side. In the case that two light quarks make a collective system by introducing a heavy
quark in a baryon, the orbtal excitation could be split into a relative orbital motion between twolight quarks and a collective motion of the light quarks relative to the heavy quark(right).

a naive picture, the pattern, if it is found, must carry infomation on a strongly correlatedcolored object, the dynamics of which should be explained by QCD. One considers the casethat a string tension between quarks becomes large enough to create a q q̄ pair in a excitedstate. In a light baryon system, a light meson (Nambu-Goldstone boson) will be easily
created at one end of the string with q, forming a lighter baryon at the other end of thestring with ”qq”. If a light qq pair forms a diquark in a charmed baryon, a string between
the diquark and a charm quark will be expanded at an excited state. This may favor a decay
to Qq̄ and qqq (if it opens energetically) and suppress a decay to Qqq and q q̄. This may one
of explanations for narrow widths of the charmed baryons.
In this respect, a charmed baryon with a charm quark (Yc ) provides a unique opportunity
to look into quark dynamics, particularly diquarks and/or diquark correlations, in hadrons.
Giving information on a structure in a hadron, we could further understand QCD in nonperturbative region. However, a limited number of charmed baryons are reported to date.
Therefore, a systematic measurement of a charmed baryon is strongly desired.
We will measure charmed baryons via the (π, D ∗− ) reactions, where the charmed baryons
are identified in missing mass spectra. We will supplement the high-momenum (hipgh-p)
beam line at J-PARC with dispersive ion optical elements so that a high-intenisty pion beamwith a resolution of ∆p/p=0.1 % can be delivered (Section refsec-hpbl. A new large acceptnce
spectrometer for the D ∗− detection is designed to achieve a missing mass resolution of as
good as 5 MeV, as described in Section III B. Charmed baryons from the ground state tohighly excited states of the excitation energy equal to ∼1 GeV will be identified in a missing
mass spectrum of the p(π, D ∗− ) reaction. Expected missing mass spectrum is demonstrated
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FIG. 2: Missing mass spectrum of the (π, D ∗− ) reaction on hydrogen is demonstrated by a MonteCalro simulation. Here, known states reported by Particle Data Group [3] are taken into account,except for the highest peak at ∼3.08 GeV/c2 , assuming a production cross section for each state

to be 1 nb.

in Fig. 2. Here, known states reported by the Particle Data Group [3] are taken into account,except for the highest peak at ∼3.08 GeV/c2 , assuming the production cross section for eachstate to be 1 nb. A number of background events can be reduced by identifying a charmed
meson production twice, namely D ∗− and D 0 in a decay chain of D ∗− → D̄ 0 + π − followedby D̄ 0 → K + π − . Details are described in Section III B.
We will measure the excitation energies and widths of the charmed baryon states, inwhich we expect to find some hither-to-unobserved states. We could deduce informtion ona diqaurk correlation from the measured level structure. In addition to the masses andwidths, the spectrometer enables us to measure some of decay branching ratios of a excited
baryon by detecting decay products(Section III B). Decay branching ratios (partial decay
widths) can be immediately obtained from the numbers of produced parent and daughter
states populated via the (π, D ∗− ) and (π, D∗− M) reactions, respectively, where M represents
the decay particles from a polulated charmed baryon. This is an advantage of the missing
mass spectroscopy. According to the simulation, angular range of the decay particle canbe covered widely so as to measure an angular distribution. This as well as the decaybranching ratio would be helpful to determine a spin of the state [13, 14]. The production
cross section must carry information on structure of produced charmed baryon through thecoupling constant and transition form factor at the NDYc and/or ND ∗ Yc vertices.
Here, we propose new charmed baryon spectroscopy by means of the missing mass method
to shed lights on the diquark.

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FIG. 3: Reaction and decay diagrams considered.
II.

(π, D̄ ∗− ) REACTION

We propose to study charmed baryons at the high momentum beam line of the J-PARC
hadron facility. Charmed baryons will be identified in the missing mass spectra of the(π, D ∗− ) reactions. Charmed baryons can be produced in a wide mass range from theground state up to highly excited states of the excitation energy as high as 1 GeV at once.
∗+
The (π − , D∗− ) reaction on a hydrogen target can populate both Λ∗+c and Σc , as illustrated
in Fig. 3-(a). This is standard. We have another choices for the beam polarity and/or thetarget (neutron in deuteron) to control the isospin of a produced charmed baryon (Fig. 3-(b)and (c)). The spectrometer system is charge symmetric, as described in Section III B. When
we choose the reaction mode (c) in Fig 3, we can measure an exotic channel, as shown in
Fig. 3-(d).
To date, there is no expereiment observed charmed baryons in a missing mass spectrumof the (π − , D∗− ) reaction. There is only a report which gave an upper limit of the crosssection, ∼270 nb at the incident pion momentum (pπ ) of 13 GeV/c in 1985 [15]. We estimate
the production cross section to be at a level of 1 nb, employing a Reggeon exchange model[16], as described in Appendix E. We therefore improve sensitivity two orders of magnitude
better than that of the previous experiment. On the other hand, the reaction cross section
with a positive kaon production, which is a potential source of background, is estimated to
be as high as 1.8 mb at pπ =15 GeVc [17]. The total cross section of π − collision to p withstrange particle production has been measured as 3.4 mb [18]. We will reduce backgroundcontamination by an order of 6 to 7 with identifying a charmed particle production twice,namely D ∗− and D 0 in a decay chain of D ∗− → D̄ 0 + π − followed by D̄ 0 → K + π − . Details
6KEK/J-PARC-PAC 2012-19
are described in Section III B
III.

EXPERIMENTAL FACILITY

A.

Beam Line Configuration

1.

Concept

The high-momentum (high-p) beam line has been designed for the E16 experiment [19] toutilize a 30-GeV primary beam. The high-p beam line branches off at the SM point locatedat the middle point of the slope in the switch yard of the slow extraction beam line. A small
fraction of the primary beam, about 1010 protons per spill, will be delivered for E16 throughthe high-p beam line. Since a production target of up to 15-kW beam loss can be placed at
SM, an intense pion beam can be produced through the beam line.
We reconsider the high-p beam line design so that high-momentum unseparated secondary
beams of sufficient intensity can be available to carry out the present experiment. The
beam line must be compatible for the use of primary and secondary beams without major
rearrangement of the beam line elements. We expect the High-p beam line performance asfollows:- The pion beam of up to 20 GeV/c to produce excited charmed baryons that we study.
- A momentum resolution of 0.1% so that a missing mass resolution can be acheived at
a level of 5 MeV.
- A Large acceptance of the beam line to achieve the intense pion beam of higher than
107 particles per second.

2.

Optical Design

The beam line layout is shown in Fig. 4. It is composed of three parts, as corresponding
to three focal points, IF, DP, and FF. In the first part, secondary beams produced at SM
are collected and focused on IF. Here, we use 4 quadrupole magnets and 1 horizontal and 1
vertical bending magnets. The first Q magnet, which determines the solid angle of the beamline, is located at 4.5 m downstream of SM, although this magnet yoke has to be considered
so as not to intercept the primary beam. A vertical bending magnet has to be placed before
IF in order to bend the beam down to the beam level of the hadron hall. The magnificationsin the horizontal and vertical directions are set to −1.591 and −2.398 at IF. The beam size
will be redefined by collimators placed at IF.

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FIG. 4: Beam line layout is shown.

In the second part, the beam is focused at DP so as to make a dispersive focus, wherea strong correlation between a beam momentum and a beam position. We employ 3 bending magnets to make a sufficient dispersion and 4 quadrupole magnets to focus the beam.
The magnifications of the horizontal and vertical directions at DP are 0.664 and 4.658, respectively. The momentum dispersion is realized as 1.031 cm/%. We employ 3 sextupole
magnets in order to eliminate second order aberrations. We expect a momentum resolutionof ∼0.1% if we measure a position of a secondary particle with a spatial resolution of 1 mm
at DP. Contribution of the beam momentum resolution of 0.1% to a missing mass resolution
is estimated to be about 4 MeV in the p(π, D̄)Λc reaction at the incident momentum of 15
GeV/c.
In the last part, the beam is focused on FF with a momentum dispersion. The magnifications of the horizontal and vertical directions at FF are −1 and −1.678, respectively. By
using three bending magnets, each of which has 6 m long pole length, and 7 quadrupoles
realize a momentum dispersion to be 1.207 cm/% at FF.
A beam envelope of the High-p beam line is calculated to the second order by TRANSPORT [20], as shown in Fig. 5. In this beam optics, the momentum resolution is estimated8KEK/J-PARC-PAC 2012-19

FIG. 5: Beam envelope calculated to the first order transport matrix.

by a ray-tracing computer simulation code, TURTLE [20]. Fig. 6 shows a strong correlationof a beam displacement with respect to the beam momentum. When we select a beam
position in a 2mm width bin, it is demonstrated that an r.m.s. width of the momentum
distribution in any bin is kept to be a level of 0.1 %. In this simulation, the acceptance ofthe beam line is estimated to be about 2 msr*%. We estimate yields of secondary particles
by the Sanford-Wang formula [21]. We assume a production angle of 2.5 degrees and a
15-kW primary beam lost at (interacted with) a plutinum target. In-flight decays throughthe beam line length of 132 m are taken into account. An intensity of 15-GeV/c negative
pions is estimated to be 6×107 particles per spill (2 sec. spill, 6 sec. interval).
B.

Conceptual Design of the Charmed Particle Spectrometer System

The purpose of experiment is to measure excited charmed baryon states of a mass region
up to about 3 GeV. To reveal the properties of excited charmed baryon states, the missing
mass spectroscopy method are mainly used in the experiment. The mass and width of those
excited states are determined by the missing mass method. The production cross sections
are measured for investigating the production mechanism. In addition, the measurement of
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FIG. 6: Dispersive beam correlation at FF is shown.

FIG. 7: Yields of secondary particles at a production angle of 2.5 degrees for a 15-kW primarybeam lost at a platinum target, calculated by the Sanford-Wang formula [21]. The acceptance andthe total length of the beam line are 2 msr*% and 132 m, respectively.

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the decay products from excited baryons such as the Yc∗ → Yc + π decay, and the analysis of
the decay chain which decays to the known states, the spin and parity of the excited states
could be also determined. The excited charmed baryon states could completely be measured
in the experiment.
In the experiment, the π − + p → Yc∗ + D̄ ∗− reaction is used. The D̄ ∗− meson decays by
the D̄ ∗− → D̄ 0 + π − channel (branching ratio of 67.7%). Then, the D̄ 0 meson decays by
the D̄ 0 → K + + π − channel (branching ratio of 3.88%). The decay products of K + andπ − from D̄ 0 and π − from D̄ ∗− are mainly detected by the spectrometer. The spectrometeris designed to detect the final state of the ”K + , π − , π − ” mode. The other decay modesof the D̄ 0 meson which have all charged particles could be also measured according thespectrometer acceptance.
The detector configuration of the spectrometer is designed to satisfy those experimental
requirements as followings;• Large acceptance for D̄ ∗− decay particles (multi-particles measurement)• Mass resolution as good as 5 MeV/c2 to search for excited charmed baryons• Particle identification (K and π) performance in a momentum of up to 10 GeV/c• High-rate capability for handling the high-rate beam.
The decay products of K + and π − from the D̄ 0 decay have higher momentum up to 10
GeV/c at the beam momentum of 15 GeV/c. Those particles are scattered to the forward
direction so that the large forward detectors are installed at both the entrance and the exitof the magnet. The soft π − from the D̄ ∗− has low momentum of less than 1 GeV/c due tothe small Q-value of the D̄ ∗− → D̄ 0 + π − decay. To keep the acceptance, it is necessary to
install the specific detectors to detect the soft π − . One of the known higher excited charmed
baryon such as Λc (2880)+ has the total decay width of 5.8±1.1 MeV [13]. The missing
mass resolution of as good as 5 MeV is necessary to measure those higher excited region
with a narrow width. This value is enough to measure the excited states having a wider
width of ∼70 MeV such as Σc (2800) [22]. The scattered particles have high momentum of
up to 10 GeV/c. Due to the limited flight length by keeping the acceptance, the scatteredparticles could not separated by the time of flight measurement. We plan to use the RICH
counter. The production cross section is estimated to a level of 1 nb in Appendix E so that
it is necessary to use the intense J-PARC beam of more than 107 Hz. For measurement of
the beam and scattered particles at the downstream of the target, the detectors which has
the high-rate capability is inseparable. The spectrometer system was designed by satisfying
those experimental requirements.

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FM magnet

Internal TOF wallp-

Ring Image
Cherenkov counter

Internal DC
Beam gas
Cherenkov

LH2 target

K+

pSSD
Fiber tracker

p-

MWDC
TOF wallInternal TOF wall

Large DC

FIG. 8: Schematic view of the proposed spectrometer
1.

Conceptual design of the spectrometer

Figure 8 shows the conceptual design of the spectrometer. For design the spectrometer,
the FM cyclotron magnet which is used in the J-PARC E16 experiment [19] is planned to
be used. The magnet has a large pole gap space and an inner space for installing innerdetectors to measure the soft π − from the D̄ ∗− decay. Those properties are suitable todesign the charmed baryon spectrometer with large acceptance. The FM cyclotron magnet
is modified for the charmed baryon spectroscopy experiment by changing the pole pieces.
The gap of the magnet pole is changed to be 1 m and the maximum field strength of 1 T isused. It corresponds to the B × L value of 2.3 Tm.
To increased the yield of the excited charmed baryon states, the long length Liquid
Hydrogen target is used. The length of the target is 570 mm which corresponds to themass thickness of 4 g/cm2 . This mass thickness was determined to the contribution of
the target energy loss straggling to the invariant mass resolution for reconstructing bothD̄ 0 and D̄ ∗− mesons. The experimental target is placed at the entrance of the magnet.
For maximizing both the acceptance and the bending angle for the scattered particles, thetarget was installed to the optimized position. In the simulation, the scattered particles are
generated isotropically inside of the target along the beam direction.
The pion beams are measured by Silicon strip detectors(SSD) for tracking and a finesegmented plastic scintillation counter for timing. This timing counter determines the timezero. The horizontal size of each segment is adjusted for operating in the single counting rate
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of a few MHz. By assuming design value of horizontal beam size of 100 mm and expecting
counting rate of 30 MHz, the size is needed to be less than 5 mm. In addition, to reject
the accidental events in the beam tracking, the scintillating fiber wall with a 1 mm pitch
segment is installed. By gating the narrow fiber timing window of ∼1 ns and comparing thehit position on the fiber wall with the tracks measured by SSD, the accidental events from
intense pion beams (30 MHz) could be rejected. The segmented gas Čerenkov counter isinstalled at the upstream of the fiber wall. For separating the beam π − from K − with thebeam momentum of 15 GeV/c, the CO2 gas Čerenkov counter is used.
For detecting K + and π − from the D̄ 0 decay, tracking detectors are installed at both theentrance and the exit of the magnet. The coverage of the forward tracking detectors for
detecting K + and π − from the D̄ 0 decay is determined from the momentum and angular
distribution by the simulation by assuming the isotropic angular distribution of the π − +p →Yc∗ + D̄ ∗− reaction in the center of mass system. The detectors at the entrance of the magnet
have the horizontal and vertical size of 400−600 mm and 200−300 mm, respectively. For
the tracking devices, SSD and a scintillating fiber tracker (1 mm pitch) are used due to thehigh-rate beam. The sizes of downstream detectors are 2000−3000 mm for horizontal and1200−1500 mm for vertical direction, respectively. The large drift chambers with smaller
drift space (∼10 mm) are used for the downstream tracking devices. The wires where thebeam pass though are inactive by not applying the high voltage. The redundancy is kept
by increasing the number of the tilted wire layers. The TOF wall has a similar size to thedownstream tracking detectors. The large downstream detectors are needed to be installed
to keep the acceptance. The PID counter is installed at the downstream of the TOF wall.
The detail of the PID counter is described in Sec. III B−2.
The inner counters are installed inside of the magnet gap. To measure the tracks ofboth soft π − from the D̄ ∗− decay and K + and π − from the D̄ 0 decay, the internal tracking
drift chambers such as planner and cylindrical types are installed at the downstream of theentrance detectors. The wires where the beam pass though are also inactive by keeping theredundancy to use enough number of the tilted wire layers. The time-of-flight of soft π −from the D̄ ∗− decay is measured by the internal TOF counters localed at the magnet gap.
By using those internal detectors, the decay particles and decay chain of higher excited Yc∗
states could be measured also, because those decay particles are scattered to the forward
direction. The decay particle measurement is described in Sec. III B−8.
2.

Particle identification

The momentum range of the scattered particle from the D̄ 0 decay is up to 10 GeV/c. The
time difference between K + and π − is estimated to be ∼60 ps for the momentum of 5 GeV/c
by using the typical spectrometer flight-path length of 4 m. The conventional time-of-flightmeasurement cannot be used for the particle identification so that the timing counters such

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FIG. 9: Geometry and radiator configuration for the HERMES RICH (a) and the Čerenkov emission angles versus hadron momentum for the aerogel and the C4 F10 gas radiators (b)as the time-zero and the TOF counters are just used for selecting the prompt timing of thescattered particles. On the other hand, the slow particles from the D̄ ∗− and Yc∗ decays could
be identified by using the time-of-flight information of the internal counters.
The fast scattered particles are identified by using the RICH counter located at thedownstream of the TOF wall. In the experiment, the hybrid-RICH system is planned to be
used. The hybrid-RICH system was used in the HERMES experiment [23]. The HERMESRICH detector consisted of the aerogel (n=1.0304) and the C4 F10 gas (n=1.00137) radiators.
By using information of both the different thresholds and the Čerenkov emission anglesof those radiators, the particles (π, K, p) with the momentum of 2−15 GeV/c could be
separated. Figure 9 shows the geometry and radiator configuration for the HERMES RICH
and the Čerenkov emission angles versus hadron momentum for the aerogel and the C4 F10
gas radiators. In the momentum range of less 3 GeV/c, the aerogel is used for the thresholds
type Čerenkov detector for separating K and π. In the momentum range from 3 GeV/c to
9.3 GeV/c, the aerogel is used for the RICH type detector for K and p, and the C4 F10 gas isused for the thresholds type detector for K and π. Above 9.3 GeV/c, the C4 F10 gas is used
for the thresholds type detector for K and p and for the RICH type detector for K and π.
For the charmed baryon spectrometer, the similar hybrid-RICH detector will be developed.
3.

High-rate and multi-particle tracking system

The intense π − beam of 6.0 × 107 /spill (30 MHz for the 2 sec extraction) is planned to be
used in the experiment. This beam intensity is over the limit of the wire chamber operation
so that high-rate detectors are needed to handle the beam. For beam measurement, the14

KEK/J-PARC-PAC 2012-19
Silicon strip detectors and scintillation fiber wall are installed. The high-rate capability ofSSD (80µm pitch and 60 mm×60 mm) is up to 108 Hz and that of the scintillation fiber isa few MHz per 1 mm segmentation. Those capabilities are satisfied under the operation by
assuming 100 mm horizontal beam and expecting total counting rate of 30 MHz.
For the track measurement at the downstream of the target, the tracking devices at theentrance of the magnet have to be operated under the conditions of both the high-rate
beam and high-rate scattered multi-particles. The total charged particle cross section ofthe π − p reaction measured at the beam momentum of 16 GeV/c [24]. From the crosssection values in Ref [24], the multi-track rate with averaged particle number of 4 tacks isestimated to be 3 M/spill by the experimental conditions (4 g/cm2 target, 6.0 × 107 /spillbeam). In this condition, both the accidental tracks and the wrong tracking connection
between tracks obtained from the entrance and exit tracking devices are expected. To avoid
the incorrect tracking, the redundant tracking system is planned to be used for the tracking
at the downstream of the target. Those three kind of the tracking devices are installed, thescintillating fiber tracker for gating the narrow timing gate, SSD for separating the tracks
with the precise spacial resolution and the internal MWDCs for distinguishing the particles
tracks and charge by using the motion in the magnetic filed of the magnet. By combining
those three racking devices, it is possible to measure the multi-particle tracks under thehigh-rate condition without the incorrect tracking. The high-rate and multi-particle tracking
system is one of the key device for the experiment.
4.

Acceptance

The acceptance of the spectrometer system was estimated by the simulation. The accepted condition are followings.
• Both K + and π − from the D̄ 0 decay pass though all the layers of tracking devices andthe TOF wall.
• Soft π − from the D̄ ∗− decay pass though the entrance tracking devices, the internal
tracking chambers and the internal TOF wall.
The acceptance which is the ratio of the number of the accepted particles divided bythat of the generated ones are shown in Fig. 10(a). The bottom figures show the momentum correlation of both generated (b) and accepted (c) particles from the D̄ 0 decay in theΛc (2880)+ produced case with the beam momentum of 15 GeV/c. The horizontal and vertical axis are acceptance and the known charmed baryon mass, respectively. The D̄ ∗− meson
is generated by assuming the isotropic and the forward (∝e−at ) angular distribution of theπ − +p → Yc∗ + D̄ ∗− reaction in the center of mass system. The decay angular distributions ofboth D̄ ∗− and D̄ 0 are isotropic in the center of mass system. By using the forward peak, thescattering angle of the generated D̄ ∗− is less than 3◦ so that due to the large opening angle of15

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FIG. 10: (a): Acceptance for D̄ ∗− as a function of the missing baryon mass. D̄ ∗− is isotropicallygenerated in the CM system. Momentum distributions of K + versus π − from D̄ 0 generated (b)and detected (c) in the case of the Λc (2880)+ production.

the D 0 decay, the acceptance is decreased in the higher mass region. The acceptance of theD̄ 0 decay particle detection is mainly determined by the gap of the FM cyclotron magnet.
When K + and π − from the D̄ 0 decay are accepted, ∼90% of soft π − from the D̄ ∗− decay
pass are detected by the internal detectors. Those soft π − s have a momentum of 0.3−1.1
GeV/c and are scattered to the polar angle of 0◦ − 8◦ . By including the decay process of
K + and π − s, the acceptance is decreased to be ∼75%. The decay factor of K + and soft π −are ∼0.85 and ∼0.90, respectively. The absolute value of the acceptance strongly depends
on the angular distribution of the π − + p → Yc∗ + D̄ ∗− reaction. If the angular distributionof the reaction is forward peak, the acceptance becomes a few times higher than that of theisotropic distribution.

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5.

Resolution

The momentum resolution, the invariant mass resolution for reconstructing the D̄ 0 andD̄ ∗− and the missing mass resolution are estimated by the simulation. The realistic materials
are input to the simulation, the liquid hydrogen for the target, the silicon for SSDs, the plastic
scintillator for the timing counters and the scintillation fibers, the drift chamber gas (Ar:isoC4 H10 ) for all chambers, and Helium gas for the gap of the magnet. For the tracking, theposition resolutions of SSD, Fiber tracker and drift chambers are assumed to be 100 µm, 200µm and 200 µm, respectively. The momentum resolution of 0.2% at momentum of 5 GeV/c
is achieved. The invariant mass resolution for reconstructing the D̄ 0 and D̄ ∗− are estimatedto be 4.6 MeV and 0.71 MeV, respectively. The contribution of the target material effect tothe invariant mass resolution of the D̄ 0 and D̄ ∗− are 2.4 MeV and 0.53 MeV, respectively.
The estimated invariant mass resolutions are mainly determined by the target ∆E straggling.
The missing resolution by assuming the production of the ground state (Λc ) and the excitedstate (Λc (2880)+ ) are estimated to be 9.6 MeV and 5.5 MeV, respectively. In the case of theΛc (2880)+ production, the contributions of the missing mass resolution is estimated from2
∆M 2 = ∆2Beam + ∆2Spec + ∆2θ + ∆Etarget, where the first term is the mass resolution comingfrom the momentum resolution of the beam line and the second is that of the spectrometer.
The third term comes from the resolution of the scattering angle and the last term fromthe target ∆E straggling. The contributions of the momentum resolution of the beam line
and the spectrometer including scattering angle resolution are estimated to 3.6 MeV and 3.9
MeV, respectively, where that of the target ∆E straggling is 1.5 MeV. The contribution of
the momentum resolution of the spectrometer and the scattering angle is balanced to thatof the beam line. The required resolution are found to be achieved.
6.

Background Event

In the experiment, the final state of the ”K + , π − , π − ” mode is detected by the spectrometer. All reaction events which include this mode could be background of the mass
spectra. There are little information about those background processes of the π − p reactionin the momentum region of 10−20 GeV/c. The total cross section of the π − p reaction
at the beam momentum of 16 GeV/c is 25.6 mb [25]. At this momentum, the inclusive
strangeness production cross section is 3.4 mb [18]. In addition, the Ks0 production withmore than 4-charged tracks which could include the ”K + , π − , π − ” mode has a cross sectionof 1.1 mb [26]. Therefore, the total cross section of a few mb has to be assumed to estimate
the background.
The background events are estimated by the simulation. To produce background events, asimulation code, JAM [17], and an isotropic phase space distribution are used for comparison.
JAM (Jet AA Microscopic transport model) code is used for the background estimation of17

KEK/J-PARC-PAC 2012-19

K *0

FIG. 11: Reconstructed mass spectra from K + and π − (D̄ 0 ) (a,b) and D̄ 0 and soft π − (c,d) in thecases of JAM (a,c) and 6-body (b,d).

the heavy iron collision experiment. The code includes many elemental processes, such asp p, π ± p and so on. The JAM code covers the low energy range of 1-20 AGeV so that we
employ this simulation code. For the background of the isotropic phase space distribution,
the combination of the particles including the ”K + , π − , π − ” mode are randomly assigned.
Then, those particles are generated by the N-body(5−7 bodies) kinematics which follows
the phase space.
Figure 11 shows the background distribution for the invariant mass of D̄ 0 and D̄ ∗− . For
reconstructing the D̄ ∗− mass, the D̄ 0 mass is assumed. For comparison, both the simulation
result by JAM and the 6-body random background are shown. Due to the processes included
by JAM, the clear K ∗0 peak is observed in the spectrum. Figure 12 shows the background
distribution for the missing mass spectra. By the JAM code, the average number of produced
particles in an event is ∼8 so that the momentum of each particle is lower than that of the
6-body random background. The number of the background events of the higher mass region
are relatively larger than that of the lower region.
In the JAM code, the total cross section of the background processes which include the”K + , π − , π − ” mode is 1.8mb. For the initial value, we employ this total cross section for
the estimation. The number of the background events are estimated to be 3.7×1011 byconsidering the experimental conditions (4 g/cm2 target, 6.0 × 107 /spill beam, 100 days
beam time). The trigger rate is roughly estimated by the JAM simulation. By assuming the18

KEK/J-PARC-PAC 2012-19

FIG. 12: Missing mass spectra for the background events. (a,c): JAM and (b,d): 6-body.

PID efficiency of 100%, the trigger rate is estimeted to be 13 k/spill. This value is just theaccepted number of events from the JAM background. If the 2.0 sec extraction is assumed,
the trigger rate becomes 6.5 kHz.
The reduction of the background is tested by the simulation. In the experiment, theinvariant mass of D̄ 0 and D̄ ∗− meson are reconstructed step by step. This analysis method
is called, ”D ∗ tagging.” By using the D ∗ tagging, the background events can be drasticallyreduced because the combinations of the background events which enter the mass gate are
drastically decreased. As shown in Fig. 13, by gating both the D̄ 0 and D̄ ∗− mass of the 2.5σ
region, the background reduction factor which includes the acceptance is 10−7 and 10−6
for JAM and the 6-body random background, respectively. The narrow mass gate by thehigh resolution spectrometer is also inseparable for the background reduction. Finally, thenumber of the background events are reduced to be 3.7×104 − 105 .
7.

Missing Mass Spectra

By assuming reduction factor of 10−7 and 10−6 , the missing mass spectra with known
charmed baryon resonances are generated. For the production of charmed baryon states, thecross section of 1 nb and is assumed with the PDG mass and width. The events are generated
by assuming the isotropic angular distribution of the π − + p → Yc∗ + D̄ ∗− reaction in thecenter of mass system. Figure 14 shows the missing mass spectra simulated with signal and19

KEK/J-PARC-PAC 2012-19

FIG. 13: Two dimensional plots of reconstructed D̄ ∗− and D̄ 0 masses for JAM and 6-body background events (a,b). By applying the D ∗ tagging, only a part of the background events remain in
the selected mass region (c,d).

background events. The background shape generated by JAM is assumed and the numberof the total events is generated to be that of the reduced ones. For the higher excited region(2.65−3.10 GeV/c2 ), the significance of the charmed baryon states is estimated by assuming
the decay width. Figure 15 shows the significance of the total cross section of 1 nb (∼1000
counts) in the case of the reduction factor of 10−6. By changing the decay width, we foundthat the reduction factor of less than 10−6 is necessary to find out the wider decay widthstate.
For reducing more background, the forward proton detection is applied. The proton fromthe decay of the charmed baryon states has higher momentum due to the large momentum
transfer. On the other hand, the proton from the background has lower momentum. Those
protons are mainly produced by the multi-meson production so that the momentum transfer
is smaller than that of the charmed baryon production. By detecting the forward proton, thebackground events generated by JAM is reduced to be ∼1/10. The signal from the charmed
baryon states is also reduced due the proton decay breaching ratio of 50%. By optimizing
the acceptance for the forward proton, the signal to noise ratio could be improved more. In
the case of the total production cross section of 1 nb, the background reduction factor of
10−6 is the limit to observe the higher excited charmed baryon states with a wider width.

20

KEK/J-PARC-PAC 2012-19

FIG. 14: The missing mass spectra simulated with signal and background events. The masses andwidths of charmed baryons are assumed as reported in the PDG [3], except for the heaviest one at
3.08 GeV (this is artificial). (a,c): Missing mass spectra for the background events reduced to be10−7 . (b,d): Missing mass spectra for the background events reduced to be 10−6 .
8.

Measurements of decay products from excited baryons

The measurement of the decay products from excited baryons such as the Yc∗ → Yc + π
decay, and the analysis of the decay chain which decays to the known states, the spin andparity of the excited states could be also determined. The produced excited charmed baryon
has large momentum in the beam direction so that decay products of these baryons still canbe detected in the forward region. Figure 16 shows the π + angular distribution in thecenter of mass system (cosθcm ) from the Λc (2940)+ → Σc (2455)0 + π + decay. The angular
distribution of the Λc (2940)+ decay is isotropic in the center of mass system. By detecting
the forward decay particles, large fraction of the angular distribution can be measured.
The momentum vector of the excited charmed baryon state is measured by the missing
mass spectroscopy. By measuring the decay products such as π ± , the mass of the daughter
charmed baryon state can be determined. The mass resolution for detecting those decay
modes is estimated to be 10 MeV. It is small enough to measure the daughter charmed
baryon state.

21

KEK/J-PARC-PAC 2012-19

FIG. 15: The significance of the total cross section of 1 nb (∼1000 counts) in the case of the
reduction factor of 10−6 . The case of the different mass window are also shown.
9.

Summary for the spectrometer

The conceptual design of the charmed baryon spectrometer were described in this section.
The spectrometer was designed for the missing mass spectroscopy experiment and also the
decay products for the Yc∗ → Yc + π decay could be detected. The excited charmed baryon
states could completely be measured systematically. For the experimental apparatus, there
are the high-rate detectors for tracking and the hybrid-RICH counter for the particle identification. By using a large detectors with the FM cyclotron magnet, the acceptance wasachieved to be 10%. The momentum resolution was estimated to be ∆p/p=0.2%. The
invariant mass resolution of 4.6 MeV and 0.71 MeV for D̄ 0 and D̄ ∗− were obtained, respectively. The missing mass resolution of 5.5 MeV was achieved for the Λc (2880)+ production
case. The background events were estimated by using the JAM code and the isotropic phasespace distribution. The reduction factor was estimated to be less than 10−6 by using theD ∗ tagging method. In the case of the total cross section of the background of 1.8 mb, wefound that the reduction of less than 10−6 is necessary for the measurement of the higher
excited state charmed baryons with production cross section of 1 nb. The acceptance of the
decay product detection was estimated. The large fraction of the angular distribution canbe measured by the forward detection of the scattered particles. The mass resolution for detecting those decay modes is estimated to be about 10 MeV. The experimental requirements
are found to be achieved.

22KEK/J-PARC-PAC 2012-19

FIG. 16: The π + angular distribution in the center of mass system (cosθcm ) from the Λc (2940)+ →Σc (2455)0 + π + decay.
IV.

BEAM TIME REQUEST

Below, we estimate an yield of a charmed baryon. The pion beam intensity and thetarget thickness of hydrogen are assumed to be 6×107 and 4 g/cm2 , respectively. The
decay branching ratios of D ∗− → D̄ 0 π − and D̄ 0 → K + π − , 0.67 and 0.039, respectively,
should be taken into account [3]. The live time of the data aquisition is assumed to be
0.9. We estimate the tarcking efficiency of the MWDCs to be 0.7. The efficiencies ofpion and kaon identifications are obtained as 98 % about 93 % for the RICH counter of
HERMES [27]. Then, the estimated yields of a charmed baryon are 2.3∼6.8 events/day/nb,
according to the acceptances of 7∼21 %, as described in Section III B-4. We think thatangular distribution with having a peak at a forward angle in the (π, D ∗− ) is more likely thanisotropic distribution, as we estimate the reaction cross sections by equations in Appendix E.
Here, we just take an average of above estimations for beam time request. We expect 450
events for a state having a cross section of 1 nb in a year (100 days). It is the first goal forthe proposed experiment to accumulate more than 1000 events so that a state with a widthof 100 MeV can be observed at a better significance, as shown in Fig. 15.
V.

ORGANIZATION

The proposed experimental project is based on the Memorundom of Understanding on Research Collaboration amang RCNP, KEK-IPNS, and the J-PARC Center. RCNP will sharenot only a certain amount of the facility cost but also of human resources for construction
and operation. The project team is expected to be in charge of collecting collaborators and23

KEK/J-PARC-PAC 2012-19
conducting experimental research programs there. The authors of the present proposal are
to be the core members of the project team.
Once the present facility is prepared, many of hadron/nuclear physics experiments canbe carried out. For example, spectroscopic studies of nucleon and hyperon resonances via
the (π, ρ) and (π, K ∗ ) reactions are described in Appendix F
It should be mentioned that the present proposal is based on intensive discussions witha theory group in hadron physics [29]. . We will strengthen this collaboration further more
to extract fruitful physics from this project.
VI.

COST ESTIMATION

Construction cost of the proposed experimental equipment is estimated below:+ High-p Beam line:
KEK will be asked to make a budget request of 19.8 Oku-yen for a construction of
the High-p beam line to MEXT. This beam line is requested for the E16 experiment[19] to utilize a 30-GeV primary beam. The beam line can be compatible for the useof primary and secondary beams by adding 6 quadrupole and 3 sextupole magnets.
Additional cost is estimated to be about 2.1 Oku-yen. The cost for 8 power supplies
is to be about 0.8 Oku-yen if they are newly constructed. We need a primary target
system of 15-kW beam loss. An indirect water cooled target system is expected to
be placed, as used for the T1 target at a primary beam power below 50 kW that
corresponds to about 25-kW beam loss. Four bending magnets are placed in series
with the 15-kW target being the center so that a negative pion beam extraction at
a production angle of 2.5 degrees is realized with the so-called Beam Swinger Optics[30].
+ Beam Line Detectors and Charm Particle Spectrometer:
According to the design of the beam line detectors and the spectrometer system, as
descirbed in Section III, we estimate the cost.
amount unit price total price(104 yen) (104 yen)
Beam Line Detectors
Focal Plane SFT
Gas Cherenkov (CO2 )SSD
SFTTiming Counter
Spectrometer Detectors
SSD

2
1
12
2
1

100
500
500
100
220

200
500
6000
200
220

48

500

24000

24

KEK/J-PARC-PAC 2012-19
SFT
MWDC
Timing Counter
RICH
Cabling
34 twisted-pair cables
Coax. cables
Digitizing Electronics
32ch TDC
32ch HRTDC
32ch ADC

9
4
3
1

478
2947
821
20000

4302
11788
2463
20000

1545
12636

4
2

6180
25272

773
139
139

50
70
70

38650
9730
9730

A labor cost is not included above.

25

KEK/J-PARC-PAC 2012-19
APPENDIX A: QUARKS AND DIQUARKS
1.

Quark model classification

Ingredients of the quark model are the constituent quarks which move in a single particle
potential of confinement. The constituent quarks are different from the bare quarks of the
QCD Lagrangian. Due to the strong interaction the mass of the light quarks is dynamicallygenerated; ms ∼ mu ∼ md ∼ 300 MeV. Due to their rather large values and similarity
among u, d, s quarks, quarks are assumed to be treated in a non-relativistic manner withrespecting spin SU(2) and flavor SU(3) symmetries. This leads to SU(6) symmetry which isempirically very well satisfied, the basis of the constituent quark model.
Let us consider a classification of the Qqq baryons as discussed in this proposal. In
the heavy quark limit, Q behaves as a fixed center around which two light quarks movearound. Thus the dynamics is dictated by the two light quarks. Wave functions are thenthe products of spin, flavor and orbital parts. Here we consider the ground state and thep-wave excited states as an example of the classification. Extension to further excited statesis straightforward, though complicated.
Spin and flavor states are denoted by the dimensions of the representations. Thus spin
1/2 states are expressed by 2, spin 1 states are by 3, and so on. Flavor states are 3, 6, and soon, and their conjugates 3̄, etc. The two quark states are then classified by the irreducible
decomposition of two fundamental representations of the spin and flavor group;
spin : 2 × 2 = 1A + 3S

flavor : 3 × 3 = 3̄A + 6S
where the subscript shows permutation symmetry: either symmetric (S) or antisymmetric(A). Orbital states are denoted by S for the lowest s-wave state, and by λ and ρ for pwave excitations of the λ and ρ modes, respectively. Under permutation, s-wave states are
symmetric, while p-wave states are antisymmetric. The λ mode corresponds to the centerof mass motion of qq and ρ to the relative motion of qq. Because the color state of qq
is antisymmetric 3̄ in a three quark baryon, the qq must be symmetric when spin, flavor
and orbital wave functions are combined. Thus for the ground and p-wave excited states,
possible qq states are as follows:
ground :p−wave :3̄ 1 S0 , 6 3 S1
1

3

(A1)
3

1

3̄ λ1 , 6 λ0,1,2 , 3̄ ρ0,1,2 , 6 ρ1

(A2)

where the notation is D 2S+1 LJ , with D flavor representation, S spin value, L orbital angularmomentum and J the total angular momentum. In the naive quark model, all the states of(A1) and those of (A2) are degenerate, separately. This is shown in the left of Fig. 17

26

KEK/J-PARC-PAC 2012-19
Qqq baryon
quark modelρq

Q[qq] baryon
with diquark correlations
q

q

λ
Q

λ
Q

33ρ0,1,2, 61ρ1
31λ0, 63λ0,1,2

single quark
mode
1

3 S0, 63S1

ρ qchiral partners

33ρ0,1,2

33ρ0,1,2, 61ρ1

6 ρ1
1

L=0
1/2-, 1/2-, 3/2-, 3/2-, 5/2P----Q
L=0
1/2-, 3/2V----Q

ρ mode63λ0,1,2

31λ1, 63λ0,1,2

diquark
motionλ mode31λ1

spin-spin
31S0, 63S1

63S1

L=1

A----Q 1/2-, 1/2-, 3/2-, 3/2-, 5/2L=1
1/2-, 3/2S----Q
L=0
A----Q 1/2+, 3/2+

1

3 S0

L=0
1/2+
S----Q

FIG. 17: Expected Qqq spectrum in a single particle picture of the quark model (left) and thosewith diquark correlations (middle and right). From the left to the middle, orbital motion of λ islowered due to the collectivity of the diquark motion. From the middle to the right, spin correlations
are turned on among light quarks qq. Symbols S, P, V and A are for the scalar (1 S0 ), pseudoscalar(3 P0 ) vector (3 P1 ) and axial-vector (3 S1 ) diquarks, respectively.
2.

Diquarks

In some cases, it has been known that diquarks are useful ingredients to describe hadrons
at low energy. A well known example was presented by Jaffe long time ago to explain thelight scalar mesons, σ(600), κ(800), f0 (980) and a0 (980) [4]. The mass ordering of thesemesons are not explained by a simple q̄q structure, but is naturally done so by assuming[qq][q̄ q̄] structure, where color anti-symmetric 3̄ scalar diquark [qq] is adopted. Because of
the Pauli principle, the flavor of this diquark is determined as anti-symmetric 3̄, and so isdenoted as 3̄ 1 S0 in the present notation.
Table 1 summarizes relative strengths of the color-magnetic (spin dependent) interaction
α λa (i) λa (j)~σ (i) · ~σ (j) .
VCS = −
2
2
ij mi mjX

(A3)

for all possible qq states, assuming that the orbital motion of the relative qq is the groundstate. In three quark baryons, only half of the listed states, 3 1 S0 and 6 3 S1 , are allowed27

KEK/J-PARC-PAC 2012-19
due to the Pauli principle. The other two diquarks are, however, allowed for exotic hadrons.
Due to the interaction (A3), the scalar diquark 3 1 S0 is expected to be lighter than theaxial-vector diquark 6 3 S1 .
Now, as Eq. (A3) shows, if the interaction depends on the inverse mass of the quarks, thediquark correlation becomes more relevant for light quark pairs, while if either one or bothquarks are heavy, the correlation is suppressed.
TABLE I: Matrix elements of the color-spin operator in various diquark systems.
qq 3̄ 1 S0 6 3 S1 6 1 S0 3̄ 3 S1
−1/2 +1/6 +1/4 −1/12

It is a general feature that correlations resolve degenerate spectrum in many-body systems. An example is shown in Fig. 18 for nuclear levels expected in the simple harmonic
oscillator model which is compared to more realistic cases, where the degenerate levels areresolved as more correlations are turned on.

N=30f, 1p

1p 1/20f 5/2
1p 3/2

1p
0f

N=2

N= 1

0d, 1s1s0d0d 5/20p

0p 1/20p 3/20p

0s

0s

Harmonic Oscillator

Wood-Saxon

N= 0

0f 7/20d 3/2
1s 1/20s 1/2+ Spin-orbit

FIG. 18: Nuclear levels expected in three different potentials, and qualitative pattern of resolving
the degeneracy when correlations are introduced.

28

KEK/J-PARC-PAC 2012-19
3.

Chiral partners

Chiral symmetry is one of the fundamental symmetries of QCD, and is relevant for lightflavor quarks. In the present world, it is spontaneously broken and is considered to be
responsible for the mass generation of light flavor hadrons. It is responsible for the massesof the constituent quarks.
The chiral symmetry transformations are
q → exp(iγ5 θt)(A4)where θ is a set of transformation parameters and t the generator of the light flavor transformations. The product θt is understood to be an inner product over the components of
the adjoint representations of the flavor group.
In a relativistic construction, five kinds of Lorentz bilinear forms of diquarks are possible;q̃q, q̃γ5 q, q̃γµ q, q̃γµ γ5 q, q̃σµν q. Here q̃ = q T iγ0 γ2 γ5 which transforms as q̄ under the Lorentz
transformation. Now those bilinear forms are related by the chiral symmetry transformations(A4);
q̃q ↔ q̃γ5 q,q̃γµ q ↔ q̃γµ γ5 q

(A5)
(A6)

The states which transform under chiral symmetry transformations are called chiral partners.
In the non relativistic notation, there is correspondencesq̃q → 1 S0 (S),q̃γµ q → 3 P1 (V ), q̃γµ γ5 q → 3 S1 (A), q̃γ5 q → 3 P0 (P ) .

(A7)

Here shorthand notations S, V, A, P are also denoted. By combining them with anotherquark, we can form chiral partner baryons. They are denoted by circles of skid and dashedlines in Fig. 17.
As an empirical fact, chiral partners have a mass difference about half GeV. This seems
universal by choosing possible candidates of chiral partners in light flavor hadrons as shownin Fig. 19. In the quark model, the P and V diquarks requires an internal p-wave excitation.
Whether such excited diquarks survive in hadron structure is an important question.
APPENDIX B: THRESHOLD EFFECTS AND HADRON DYNAMICS
1.

Opening of hadron thresholds

Excited baryons are strongly renormalized by the dynamics of ground state hadrons.
The opening of hadron thresholds primarily gives the decay width to excited states. Not
only that, multi-hadrons can become constituents of excited states as hadronic molecules,
if correlations among hadrons are sufficiently strong. Hadronic correlations are primarily
29

KEK/J-PARC-PAC 2012-19
GeV

Baryons

Mesons(1670)

1.5
1

1.0(~ 600)1

a1 (1260)

(770)

1

1

f 1 (1285)

(780)

0
0

(1300)

K1 (1400)
1(1295)(1190)

K1 (1270)a0 (980)
f 0 (975)

1
2

1

*

K (890)(1750)(1120)1
2

3
2

N(1535)3
2(1700)(1232)

N(939)

0

0.5
0

(139)

FIG. 19: Expected chiral partners of hadrons with opposite parities.

driven by a long-range dynamics among hadrons, in contrast to the short range quark-gluon
dynamics in the confinement scale. The understanding of the interaction among hadrons
is then important to generate exotic hadrons and multi-quark states. These features are
discussed actively also in the charmonium sector, where many findings have been recently
accumulated above the open charm D D̄ threshold [31]. In the following, we discuss various
issues which are accessible in charmed baryon spectroscopy.
2.

Comparison of charm with strangenessTo see the importance of threshold effects in the excited baryon spectroscopy, let uscompare the threshold energies and masses of excited hadrons in strangeness S = −1 sector
and charm C = +1 sector (Fig. 20). As seen in the figure, the level ordering of the excitedstates of uds hadrons (Λ, Σ) is the same as that of the udc hadrons (Λc , Σc ). However, theirenergies relative to two-body thresholds are quite different. To understand these features, let
us consider the symmetries of QCD. In the massless limit mq → 0, hadrons are constrained bychiral symmetry, and in the limit mq → ∞, heavy quark symmetry becomes manifest [32].
Although both of them are approximate symmetries for charm and strange sectors, theremnant of the idealized limit can be found in the observed pattern of the spectrum.
For instance, it is instructive to compare the mass difference of 1/2+ and 3/2+ states ofΣ and Σc :MΣ,3/2+ − MΣ,1/2+ ∼ 192 MeV ≫ MΣc ,3/2+ − MΣc ,1/2+ ∼ 65 MeV(B1)This mass difference stems from the spin-spin force which is suppressed when the quark
mass is large, as a consequence of the heavy quark symmetry. Because of the reduction of
the mass difference, the ground state of Σc lies above the πΛc threshold. At the same time,
the threshold energy of πΣc appears higher than the 3/2+ state. As a consequence, theground state of Σc can decay via strong interaction, which is forbidden in the strangeness30

KEK/J-PARC-PAC 2012-19
DN
3/2−

2700

Energy [MeV]

1500
1400
1300

3/2−
ΚΝ
πΣ

1/2−

1/2−

3/2+

πΣc

2600

3/2+
2500

1/2+
πΛc

πΛ
1200
1100

2800

2400

1/2+
1/2+
Λ

2300

1/2+
Σ

Λc

Σc

FIG. 20: Comparison of the threshold and excited state energies of the strangeness S = −1 andcharm C = +1 sectors.

sector. In addition, the excited state of 3/2+ Σc cannot decay into the πΣc channel whichis allowed in the strangeness sector. Thus, it is possible to study the effect of the openingof new threshold through the comparison of Σ and Σc states.
Another example can be seen in the negative parity excited states of Λ (Λc ). Thesestates can couple to the πΣ and K̄N channels (πΣc and DN channels). If we compare thethreshold energy differences of the K̄N-πΣ system and the DN-πΣc system, we find
EK̄N − EπΣ ∼ 104 MeV ≪ EDN − EπΣc ∼ 213 MeV(B2)This can be understood by chiral symmetry. π and K̄ can be regarded as Nambu-Goldstone(NG) bosons, while D meson cannot be so, since charm quark is too heavy to be a chiralfermion. The NG boson nature of K̄ reduces its mass from the naively expected value in theconstituent quark model. Thus, the mass difference between K̄ and D should be much larger
than the mass difference between Σ and Σc , which leads to the threshold energy differencein Eq. (B2). Because of the change of the threshold energies, the 3/2− state of Λc is foundbelow the DN threshold, and the 1/2− state comes close to the πΣc threshold.
In this way, the pattern of the threshold energies in charm sector is different from thestrangeness sector. Although the quark mass in QCD is not an adjustable parameter, comparison of charm and strangeness sector enables us to extract the information of threshold
effects in the structure of excited hadrons.
APPENDIX C: CHARMED MOLECULESIn this section we consider hadronic molecules containing heavy quark as candidates of
exotic hadrons. Two examples are discussed; one is the exotic baryon formed by D̄N [33, 34]31

KEK/J-PARC-PAC 2012-19
and the other the dibaryon formed by Λc N [37]. A common feature of these states are thatthe main interaction of the two hadrons is dominated by the one pion exchange. The
couplings such as D̄ ∗ D̄π and Σc Λc π are responsible for the interaction. Note that the D̄Nsystem is truly exotic which requires minimally five quarks. We may be able to consider a
DN system, but it requires couplings to the genuine quark states such as cud, where moretheoretical study is needed.
In the heavy quark sector, molecular states are more likely to be formed by two reasons.
One is that the kinetic energy is suppressed because of larger reduced mass. The other is thatthe spin degeneracy of heavy hadrons renders significant coupled channel effects. In fact,D̄ ∗ and D̄ are degenerate spin multiplet in the heavy quark limit, and so are Σc (1/2+ ) andΣ∗c (3/2+ ). Therefore, coupled channel effects of D̄ ∗ N in the D̄N system, and of Σc (1/2+ )Nand Σ∗c (3/2+ )N in Λc N is a driving force to make bound and resonance states.
For the D̄N systems, the interaction was constructed by using the D ∗ decay into Dπ as
well as the well controlled πNN coupling [34]. The results for the coupled channel analysis
for the D̄N and BN systems are shown in Fig. 21, where analysis was made both forthe charm and bottom systems. There are several bound and resonant states with similar
pattern in the two flavor systems. As anticipated, bottom systems have more strongly boundand low lying resonant states due to more attractions.

FIG. 21: Low lying bound and resonant states of the exotic D̄N and BN systems.

For the Λc N systems, the interaction between the charmed baryon and the nucleon was
first studied in Ref. [35], when the authors employed the meson-exchange potential approach.
Further studies carried out by Bando and Nagata [36] found that both Λc - and Λb -nuclear
bound states may exist for A ≥ 4, while no two-body bound state was found. On the other
hand, recent studies [37] with the modern effective theory with chiral symmetry and heavyquark symmetry have shown that it is plausible to have Λc N and also Λc Λc bound states. The
32

KEK/J-PARC-PAC 2012-19
results show significant mixings of the Σc and Σ∗c baryons in the wave functions (Fig. 22), for
the J P = 0+ (Λc N(1 S0 ), Σc N(1 S0 ), Σ∗c N(5 D0 ) channels) bound state of the binding energy
6.16 MeV (left) , and the J P = 1+ (Λc N(3 S1 ), Σc N(3 S1 ), Σ∗c N(3 S1 ), Λc N(3 D1 ), Σc N(3 D1 ),Σ∗c N(3 D1 ), Σ∗c N(5 D1 )) bound state of 7.52 MeV (right). The strong D-wave mixings are
due to the tensor force in the one-pion exchange interaction. The same mixing phenomenonis also found in the D̄N systems [34].
Channels

Channels

FIG. 22: Radial wave functions of various coupled channels of the charmed dibaryons.

APPENDIX D: ROPER LIKE STATE OF CHARMED BARYON

In naive constituent quark models, the orbital angular momentum of constituent quarks
can be excited with less energy than the nodal excitation. Consequently, the first excitedstate of a baryon is expected to have a negative parity. This expectation is, however, notrealized in the actual spectrum of the light-quark baryons; the first excited state, called
the Roper resonance, has a positive parity, while the negative parity N ∗ appears as thesecond excited state. This “inverse phenomena” in the N ∗ spectrum, the “Roper problem”,
is known as a long standing problem of the hadron spectroscopy (the “Roper problem”).
A number of attempts based on static hadron models has been made to resolve the“Roper problem”, but up to now any of those has not succeeded to give a satisfactory
answer. Though other qualitative features of the low-lying N ∗ spectrum can be understoodreasonably well in the constituent quark picture, the “Roper problem” raises serious question
on how well the constituent quarks can be used as a dynamical degrees of freedom.
Recent dynamical coupled-chanels analyses of meson production reactions have revealed
that the hadron dynamics may produce sizable mass shifts with a few hundred MeV for theN ∗ energy levels obtained from the constituent quark models [38]. This suggests that the“Roper problem” in the N ∗ spectrum could be naturally explained by taking into accountthe hadron dynamics. The large width of the N ∗ , however, implies that dispersive effectcompletely mixes up the naive picture of the constituent quark models. Therefore, it isdifficult to identify essential degrees of freedom to describe baryon properties, as far as one
33

KEK/J-PARC-PAC 2012-19
studies the light-quark baryons only. On the other hand, the widths of heavy baryons arevery small (∼ a few MeV) compared with the light-quark baryons. Thus the “contamination”
from reaction dynamics is expected to be much suppressed for heavy baryon spectrum. The
heavy baryons will be an ideal laboratory for examining if the constituentquark picture of
baryons is justified and for clarifying many questions which cannot be answered from thelight-quark baryons.
The spectrum of the Qqq baryons is shown in Fig. 23. One can see that a few low-lying
states could be understood in a simple picture, though spin-parity of them is not measured.
Let us assume that the heavy baryons consist of a heavy quark Q and a “diquark” (baryon
number 2/3 system) with the spin-parity S P and the relative orbital angular momentum L.
In this picture, the ground states Λc , Λb , and Ξc have S P = 0+ and L = 0. The first andsecond excited positive parity states with J P = 1/2+ , 3/2+ (Σc , Σb and excited states ofΞc ) can be interpreted as baryons made of a diquark with S P = 1+ and L = 0. Then, thenext pair of excited states with the negative parity (J P = 1/2− , 3/2− ) can be assigned as
the first orbital excited states with L = 1. The excitation energies of them are almost thesame for Λc and Ξc . Within this naive quark-diquark picture, the Roper states are assigned
as the first nodal excitations of the diquark with S P = 0+ and is expected to appear with
400-700 MeV of the excitation energy for Λc . Therefore, the most crucial and urgent testof the constituent quark picture is an experimental identification of this correspondent of
the Roper resonance in the heavy baryon sector. A precise determinaiton of the excitationenergy is also important because the nodal excitation energies purely reflect dynamics of
the underlying theory, QCD.
In the excitation energy region between 400 and 700 MeV, many baryon states may still
be unobserved in addition to the Roper resonance. For example, there is also a possibility
that the heavy baryons containing negative-parity diquarks (S P = 0− , 1− ) with L = 0 could
be found in the same energy region as the Roper-like state. On the other hand, at present
three baryons are observed for the Λc and Σc excited states as plotted in Fig. 23, while
the spin and parity of only one of the three states (5/2+ ) have been determined from theexperiment.
In conclusion, the experimental identification of the spectrum and spin-parity quantum
numbers for the Λc and Σc excited states up to 700 MeV excitation energy will be very
important for establishing a solid picture of baryons.
APPENDIX E: p(π, D ∗− )X REACTION CROSS SECTION

To estimate a cross section of a charmed baryon (Yc ) in the p(π, D ∗− )Yc reaction, we
employ a Reggeon exchange model based on the Quark Gluon String Model [16]. A cross34KEK/J-PARC-PAC 2012-19
700

?
+
5/2

600

[MeV]

500

?

+
0

L=0,N=1
Q
1/2+

400

-

300

3/2
1/2

200

+

(’Roper’)

+
0

3/2

1/2+

100

L=1
Q
1/2-,3/2-

+
1

L=0
Q
1/2+,3/2+

+

1/2

0

Λc, ΣcΛb, Σb

Ξc

+
0

L=0
Q
1/2+

FIG. 23:section (σ(s)) is expressed as a function of the Mandelstam variable, s;"#1σ(s) = Cdt
g12 g22 |F (t)|2|s/s0 |2α(t) ,cm
264πs(pm )t0
2
2|F (t)| = exp (2R t),
Z t1

s0 = (mM + mB )2 ,

(E1)
(E2)
(E3)

where α is a Regge trajectory of an exchanged Reggeon in a binary reaction (Fig. 24-right),
taking a non-linear Regge trajectory as a function of the Mandelstam variable t into accout[39–41]. A parameter R2 represents a slope parameter, by which the Form Factor (F (t)) of
the t-channel reaction is characterized. Parameters g1 and g2 are coupling constants at thereaction vertice to the Reggeon. A scale parameter s0 is taken to be the threshold energyof a binary reaction, thus mM and mB are masses of scattered particles, respectively. We
demonstrate that this formula reproduce energy dependences of various binary reactions.
Fig. 24-left shows measured cross sections of strange meson and baryon production in a pioncollision with a proton. A solid line is calculated for R2 =2.13 (GeV/c)2 , g1 =5.8, g2 =4.5 asadopted in Ref. [39]. Just use C=0.5, the line fits the data for the (π − , K 0 ) reaction fairly
well.
Then, we estimate cross sections of the p(π, D ∗− )Yc reactions as a function of incident
pion beam mometum, as shown in Fig. 25-left. We use α for D and D∗ Reggeons shown
in Ref. [41]. We found that the cross section for the ground state Λc has a peak at aroundpπ =15 GeV/c but that for the excited state Λc (2880) greater than 25 GeV/c. On the other
hand, the pion beam intensity descreases as the momentum increases. Fig. 25-left shows a
Figure of Merit, taking a product of the intensity and the cross section. Accoding to thisfigure, the momentum dependence becomes flat at around 20 GeV/c at highly excited states.
35

KEK/J-PARC-PAC 2012-19

FIG. 24: Various binary reactions measured in strange quark secters. The solid line calculated by
the formula fits the energy dependence of the (π − , K 0 ) reaction

FIG. 25: Calculated cross sections for Λc and Λc (2880) productions in the (π − , D ∗− ) reactions.

The beam momentum should be chosen between 15∼20 GeV/c in experiment.

36

KEK/J-PARC-PAC 2012-19
APPENDIX F: AXIAL FORM FACTOR MEASUREMENT

An experimental setup for charmed baryon spectroscopy can be used for light flavor one
as well. We also plan to measure the axial vector transition form factor from nucleon to lightflavor baryon resonance. Hadron form factors describe the spatial distributions of charge andcurrent inside the hadron, and thus are intimately related to its internal structure. The fundamental understanding of the hadron form factors in terms of Quantum Chromodynamics(QCD) gives the confinement mechanism, and is one of the outstanding problems in nuclear
physics. The electromagnetic structures (vector response) of baryons have been measured so
far by using electron scattering. We will determine the axial vector transition form factor,
which corresponds to the current source of the coupling to pions (kaons), by using virtual
pions (kaons). The virtual pions (kaons) are realized by detecting the extremely forward
produced vector mesons ρ (K ∗ ) at high momentum secondary beamline at J-PARC. The(π, ρ) and (π, K ∗ ) reactions on the proton is thought to give the virtual pions and virtualkaons. The axial vector form factor can be obtained from the cross sections as a function of
the spacelike invariant momentum transfer Q2 .
1.

Form factors

Historically, the electromagnetic form factors of the proton have been measured by usingelastic electron-proton scattering, and those of the neutron have been also extracted fromelastic electron-deuteron scattering [42]. The elastic electric and magnetic form factors characterize the distributions of charge and magnetization in the nucleon as a function of spatial
resolving power. The nucleon form factors are the matrix elements of the electromagnetic
current Jµ = ψγµ ψ between the initial nucleon with a momentum p and a spin four vectors and the final nucleon with p′ and s′ , and are described ashN(p′ , s′ )|Jµ |N(p, s)i = u(p′ , s′ ) γµ F1 (Q2 ) +iσµν q ν
F2 (Q2 ) u(p, s)
2m


(F1)

where m denotes the nucleon mass, q stands for the momentum transferred to the nucleonp − p′ and Q2 = −q 2 . The electric and magnetic form factors are defined in terms of F1 andF2 as:

Q2

 GE (Q2 ) = F1 (Q2 ) −F2 (Q2 )
4m2
(F2)


 GM (Q2 ) = F1 (Q2 ) + F2 (Q2 )These form factors are interpreted as Fourier transforms of the nucleon charge and magnetization densities. The elastic form factors at low Q2 are known to approximately follow a
dipole form
1
GD (Q2 ) ∝
(F3)
!2 .
Q2
1+
0.71GeV237

KEK/J-PARC-PAC 2012-19
This behavior can be explained by a vector meson dominance model in which the virtualphoton couples to the nucleon after the fluctuation from the virtual photon into a virtual
vector meson. Figure 26 shows the GE and GM divided by GD as a function of Q2 for the
proton obtained by the Rosenbluth cross section method, and Figure 27 shows those for theneutron obtained in double-polarization experiments. The deviations from the dipole form
is important at larger Q2 . Different charge and magnetization distributions are suggested
for the proton [43–45].

FIG. 26: Data base for the proton GE and GM obtained by the Resenbluth cross section
method [46].

The excitation spectrum of the nucleon is a feature of strong interaction in the nonperturbative domain. A variety of excited baryon resonances are investigated by using πNelastic scattering and meson photoproduction experiments. The properties of these baryon
resonances have been extracted such as mass, width, and branching ratios of their decay.
The transition form factor from the nucleon to a baryon resonance B ∗ (NB ∗ form factor) is
also a fundamental property of B ∗ . The transition form factors are defined similarly to the
nucleon form factors, yet the final state is no longer a nucleon but a baryon resonance stateB ∗ , and the matrix elements become hB ∗ (p′ , s′ )|Jµ |N(p, s)i. The first trial to determine theelectromagnetic form factors for baryon resonances were made by using inelastic electron
scattering on the proton at DESY [47]. The similar inelastic electron scattering experiments
were carried out also at Stanford Linear Accelerator Center (SLAC) [48]. The decay particles
from the baryon resonance were not detected in these experiments and the form factors canbe deduced only for the isolated excited resonance ∆(1232)P33 . Recently, electromagnetic N ∗38

KEK/J-PARC-PAC 2012-19

FIG. 27: Data base for the neutron GE and GM obtained in double-polarization experiments [46].

transition form factors for many states have been obtained at JLAB/CLAS. Measurementof π + and π + π − electroproductions on the proton give the transition form factor of baryon
resonances with a mass W < 2.1 GeV and a momentum transfer Q2 < 1.5 GeV2 [49, 50].
Figure 28 shows the form factor G∗M for the γ ∗ p → ∆(1232)P33 transition obtained at
JLAB/CLAS.

FIG. 28: Form factor G∗M for the γ ∗ p → ∆(1232)P33 transition relative to 3GD [49].

The nucleon axial form factor can be defined with the axial current Aµ = ψγµ γ5 ψ between
the initial and final nucleons:qµ γ5hN(p , s )|Aµ |N(p, s)i = u(p , s ) γµ γ5 GA (Q ) +GP (Q2 ) u(p, s).
2m
′

′

′

′



39

2



(F4)

KEK/J-PARC-PAC 2012-19
The axial form factors characterize the distributions of the axial charge in hadrons at low
Q2 as a function of spatial resolving power. A pion exchange plays an important role innuclear physics, and thus the distributions of the axial charge, namely the current sourceof the coupling to pions, are important to understand the hadron interaction. The Q2
dependence of GA for the nucleon is determined by two types of the experiments. One is
the quasi-elastic (QE) νN scattering (νn′ → µ− p), and the other is π + electroproduction on
the proton (ep → eπ + n) [51]. The axial form factors are approximately described as
GA (Q2 ) =

gA
Q2
1+ 2
MA

!2

(F5)

with an axial mass MA . Fitting to the QE ν-N scattering experiments gives MA = 1.001 ±0.020 GeV. The MA from the π + electroproduction on the proton is 1.013±0.015 GeV, which
agrees well with MA from the QE ν-N experiments. Fig. 29 shows the axial masses obtained
from these experiments. Recently, the axial form factors can be obtaiend by a lattice QCD
calculation [52], and the direct comparison can be made between the experiments and thecalculations.

FIG. 29: Axial mass MA extracted from quasi-elastic neutrino and antineutrino scattering experiments (left), and the axial mass MA extracted from charged pion electroproduction experiments(right) [51].

The axial NB ∗ transition form factors are also defined similarly to the electromagnetic
NB ∗ form factors where the matrix elements become hB ∗ (p′ , s′ )|Aµ |N(p, s)i. We propose
to determine the axial NB ∗ transition form factors for the first time from the Q2
dependence of the B ∗ production yield coupling to virtual pions (kaons). Since
40

KEK/J-PARC-PAC 2012-19
the axial form factors link the strong and weak interactions through the partial conservation of axial vector current (PCAC), they are important both for the hadron and neutrino
interactions [53].
As for the strangeness sector, the structure of the Λ(1405) hyperon resonance is one of
the important issues in hadron physics. Since Λ(1405) is considered to be a quasi-boundstate of K̄N, its structure gives the K̄N interaction at low energies. The Λ(1405) has amass between πΣ and K̄N thresholds, and it decays to the πΣ channel with I = 0 by
the strong interaction. The dynamical description with coupled channels are reuired forunderstanding Λ(1405). The Λ(1405) can be predominantly described by meson-baryon
components in a coupled-channels approach based on chiral dynamics [57]. Recently, thepossibility of two resonance state composition having different coupling nature to the πΣ andK̄N channels is discussed for Λ(1405) [56, 58–60]. Experimental efforts for understandingthe Λ(1405) nature were made by measuring the πΣ invariant mass distributions for differentπΣ channels [61–64]. Since the Σ(1385) is located close to the Λ(1405), the decay particles
from the Λ(1405) must be detected. We propose to determine the axial pΛ(1405) transition
form factors where the Λ(1405) component is extracted form the isospin decomposition
between the π − p → K ∗0 X and π + p → K ∗+ X reactions.
2.

Virtual pions and virtual kaons

The virtual pions (kaons) are realized by detecting the extremely forward produced vector
mesons ρ (K ∗ ) at high momentum secondary beamline at J-PARC. The t channel process is
considered to be dominant for the pion-induced (π, ρ) and (π, K ∗ ) reactions on the proton
when the vector mesons ρ (K ∗ ) are detected at the extremely forward angles. The quantum
numbers transferred to the proton target are the same as those for pseudo scalar mesons,namely virtual pions (kaons) are considered to be exchanged. As for non-strangeness sector,
two different channels π − p → ρ0 X and π + p → ρ0 X enables us to decompose the nucleonand ∆ resonances. Both the nucleon and ∆ resonances are produced in the π − p → ρ0 X
channel, and only the ∆ resonance can be produced in the π + p → ρ0 X channel. The massof produced baryon resonances is determined by a missing mass technique in the first stage
experiment. We plan to identify the baryon resonance by detecting the decay particles
from it in the second stage. As for strangeness sector, two different channels π − p → K ∗0 X
and π + p → K ∗+ X enables us to decompose the Λ and Σ resonances. Both the Λ and Σ
resonances are produced in the π − p → K ∗0 X channel, and only the Σ resonance can beproduced in the π + p → K ∗+ X channel. Figure 30 shows the diagrams for producing virtual
pions and virtual kaons.
Since the t channel exchange is considered, the cross section becomes smaller as the incident pion momentum increases. The acceptance of detecting the forward vector mesons withthe charmed baryons spectrometer becomes higher since the decay particles from the vector

41KEK/J-PARC-PAC 2012-19
π−

ρ0

π+

virtual π−pGπNN*(Q2)

N*, ∆*π−

ρ0virtual π+pGπNN*(Q2)π+virtual Κ−
p

∆*

Κ∗0

GΚNY*(Q2)Λ*, Σ*

Κ∗+

virtual Κ0pGΚNY*(Q2)Σ*FIG. 30: Diagrams for producing virtual pions and virtual kaons. The t channel process is considered to be dominant for the pion-induced (π, ρ) and (π, K ∗ ) reactions on the proton when thevector mesons ρ (K ∗ ) are detected at the extremely forward angles. The quantum numbers transferred to the proton target are the same as those for pseudo scalar mesons, namely virtual pions(kaons) are considered to be exchanged.

mesons are boosted. The baryon mass resolution determined by the missing mass becomesworse since the momenta of the decay particles become higher. Here, the acceptance of detecting the forward vector mesons at the incident momentum 5 GeV/c has been estimated.
The reactions of interest are π ± p → ρ0 X, π − p → K ∗0 X and π + p → K ∗+ X. The ρ0 , K ∗0
and K ∗+ mesons are assumed to be detected by π + π − , K + π − , and Ks0 π + → π + π − π + . The
branching ratios of ρ0 → π + π − and K ∗0 → K + π − are 100%, 67%, respectively. The branching ratio of K ∗+ → K 0 π + is 67%, the Ks component is 50% in K 0 , the branching ratio of
Ks0 → π + π − is 69%. Therefore, the total branching ratio K ∗+ → π + π − π + is expected tobe 23%. These branching ratios are not taken into account in the acceptance estimation.
Figure 31 shows the acceptance of detecting the forward vector mesons at 5 GeV/c as afunction of the baryon mass for different momentum transfer t. The baryon mass resolution
determined by the missing mass is the worst for the π ± p → ρ0 X reaction because the momenta of the decay particles from the vector meson are higher. In the π ± p → ρ0 X reaction,
the baryon mass resolution of approximately 10 MeV is expected with the charmed baryon
spectrometer at the incident momentum 5 GeV/c.
The produced vector meson ρ0 at forward angles can be identified by detecting π + π − .
Figure 32 shows the π + π − invariant mass distribution for the π − p → π − π + n reaction at theincident momentum of 17.2 GeV/c [65]. The π + π − shows a clear ρ(770) peak together withf2 (1270) and ρ3 (1690) peaks. The differential cross sections for the π + p → ρ0 ∆++ reaction
were measured at the incident momentum of 13.1 GeV/c. The π + π + π − p final state eventswere obtained in the SLAC 82-inch bubble chamber. The differential cross section shows astrong forward peak as a function of |t − tmin | shown in Fig. 32. The slope is 20 GeV2 /c2
and the value of the spin density matrix ρ00 is large (> 0.9) for |t − tmin | < 0.15 GeV2 /c2 ,which are well described well with a conventional pion exchange model with absorption.
Here, the strategy of the GπN N ∗ (Q2 ) transition form factor determination is discussed for
instance. To extract GπN N ∗ (Q2 ), the ρ0 → ππ transition form factor Gρππ (Q2 ) is necessary.
42KEK/J-PARC-PAC 2012-19t0
2 2
t0-0.1 GeV /c
2 2
t0-0.2 GeV /c
2 2
t0-0.3 GeV /c
2 2
t0-0.4 GeV /c
2 2
t0-0.5 GeV /c60
Acceptance (%)

50
40
30
20
10
0

1

1.2

1.4
1.6
1.8
2
Baryon Mass W (GeV/c )t0
2 2
t0-0.1 GeV /c
2 2
t0-0.2 GeV /c
2 2
t0-0.3 GeV /c
2 2
t0-0.4 GeV /c
t0-0.5 GeV2/c2

2

1

1.2

1.4
1.6
1.8
Baryon Mass W (GeV/c2)

2

60
Acceptance (%)

50
40
30
20
10
0

t0
t0-0.1 GeV2/c2
t0-0.2 GeV2/c2
t0-0.3 GeV2/c2
t0-0.4 GeV2/c2
t0-0.5 GeV2/c2

Acceptance (%)

25
22.5
20
17.5
15
12.5
10
7.5
5
2.5
0

1

1.2

1.4
1.6
1.8
Baryon Mass W (GeV/c2)

2

FIG. 31: Acceptance of detecting forward vector mesons at 5 GeV/c. The upper, central, lower
panels show the acceptances as a function of produced baryon mass for the π ± p → ρ0 X, π − p →K ∗0 X and π + p → K ∗+ X reactions. The ρ0 , K ∗0 and K ∗+ mesons are assumed to be detected

43

by π + π − , K + π − , and Ks0 π + → π + π − π + . The branching ratios of ρ0 → π + π − , K ∗0 → K + π − ,K ∗+ → Ks0 π + → π + π − π + are 100%, 67%, 67% × 50% × 69% = 23%. They are not taken into

account in the acceptance estimation. The color indicates the corresponding momentum transfer(Mandelstam variable t).

0)
(1
27
ρ

3

(1
69

0)
?

f2

ρ(
77

0)

KEK/J-PARC-PAC 2012-19

FIG. 32: The π + π − invariant mass distributions for events with |t| < 0.15 GeV2 /c2 (left) [65]. The
acceptance corrected number of events are shown in the points with error bars. Differential crosssection as function of |t′ | = |t − tmin | for the π + p → ρ0 ∆++ reaction at 13.1 GeV/c (right) [66].
The lines correspond to slopes of 20 and 3.8 GeV/c. The small |t′ | is plotted in the inset.

The Gρππ (Q2 ) can be deduced from the π − p → ρ0 n reaction because Gρππ (Q2 ) is common
for different final state baryons for π ± p → ρ0 X and because the axial form factors for the
nucleon is well determined by the QE νN scattering and π + electroproduction experiments.
After Gρππ (Q2 ) is determined, the axial form factor can be determined as a function of
produced baryon mass. In the second stage, we plan to detect the decay particles from theexcited baryons, then the axial form factor can be determined for specific baryon resonances.
The similar π − p → K ∗− X reaction gives a transition form factor of a Θ+ pentaquark
baryon GKN Θ+ . Here, K ∗− meson is detected at forward angles, and it is identified by theK̄ 0 π − → (π + π − )π − decay. The evidence for the pentaquark Θ+ baryon was reported by the
LEPS collaboration for the first time [67]. A narrow peak was observed in the K + n invariant mass distribution in the γn → K − K + n reaction, and the Θ+ is a genuine exotic baryon
predicted by Diakonov et al [68]. The experimental situation for the existence of the Θ+is controversial. Many collider experiments found no positive evidence in the pKs invariant
mass distributions [69]. The CLAS collaboration searched for the Θ+ in the γp → K̄ 0 K + n
and γd → pK − K + n reactions [70]. No evidence for the Θ+ was obtained in these experiments, and only the upper limits for the Θ+ productions were given. Other experimentsby pion-, kaon-, and proton-induced reactions showed no evidence for the Θ+ production:
π − p → K − X [71], K + p → π + X [72], and pp → pK 0 Σ+ [73] reactions. At this moment, threepositive experiments exist: re-analysis of the K + Xe → K 0 pXe′ reaction by the DIANA colla44

KEK/J-PARC-PAC 2012-19
ration [74], the γd → K + K − pn reaction by the LEPS collaboration [75], and the γp → Ks X
reaction taken with the CLAS spectrometer by M.J. Amaryan et al. [76]. Since the Θ+ production seems highly reaction dependent, the formation experiments of K + n → Θ+ seem toclarify its existence. The K + beam with a momentum around 420 MeV/c is required for theformation experiments. Yet, it is difficult to obtain such a low momentum K + beam witha momentum analysis and particle identification since cτ = 3.712 m for the K + meson andalmost all the K + mesons decay before arriving at the target position. Therefore, the Θ+
search by using the π − p → K ∗− X reaction is the best way. A small K ∗ NΘ+ coupling, which
is suggested by the previous experiments, is not included in the π − p → K ∗− X reaction andthe vertex is the same as the formation K 0 p → Θ+ .

45

KEK/J-PARC-PAC 2012-19[1] For example, see textbooks by F. Close, An introduction to quarks and partons, Academic
Press, 1979; and also A. Hosaka and H. Toki, Quarks, baryons and chiral symmetry, World
Scientific, 2001.
[2] M. Oka and K. Yazaki, Prog. Theor. Phys. 66, 556 (1981); ibid. 572 (1981).
[3] J. Beringer et al., Phys. Rev. D86 (2012) 010001.
[4] R. L. Jaffe, Phys. Rev. D 15, 267 (1977); R. L. Jaffe, Phys. Rev. D 15, 281 (1977).
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51