Measurement of the cross sections of Σp scatterings

Proposalfor an experiment at the 50-GeV PS

Measurement of the cross sections of Σp scatterings

F. Hiruma, R. Honda, K. Hosomi, H. Kanda, T. Koike, Y. Matsumoto,K. Miwa(spokesperson), A. Sasaki, K. Shirotori, K. Sugihara, H. Tamura, M. Ukai,

K. Yagi, T.O. Yamamoto, Y. YonemotoTohoku University, Japan

K. Imai, Y. KondoJapan Atomic Energy Agency (JAEA), Japan

M. Ieiri, S. Ishimoto, I. Nakamura, M. Naruki, S. Suzuki, H. Takahashi, T. TakahashiM. Tanaka, K. Yoshimura

High Energy Accelerator Research Organization (KEK), Japan

T.N. TakahashiUniversity of Tokyo, Japan

S. Adachi, M. Moritsu, T. Nagae, H. SugimuraKyoto University, Japan

K. TanidaSeoul National University, Korea

J.K. Ahn, B.H. ChoiPusan National University, Korea

S. Callier, C.d.L. Taille, L. RauxIN2P3/LAL Orsay, France

Abstract

In order to test theoretical frameworks of the baryon-baryon interactions and toconfirm the “Pauli effect between quarks” for the first time, we propose an experi-ment to measure low-energy hyperon proton scattering cross sections in the followingchannels with high statistics,

1. Σ−p elastic scattering,

2. Σ−p → Λn inelastic scattering,

3. Σ+p elastic scattering.

According to theoretical models based on quark-gluon picture for the short rangepart of the baryon-baryon interactions, the Σ+p channel is expected to have an ex-tremely repulsive core due to the Pauli effect between quarks, which leads a Σ+p crosssection twice as large as that predicted by conventional meson exchange models witha phenomenologically treated short range repulsive core. In addition, measurement ofthe Σ−p channel where the quark Pauli effect is not effective is also necessary to testthe present theoretical models based on meson exchange picture with the flavor SU(3)symmetry. Thus this experiment will provide essential data to test the frameworks ofthe theoretical models of the baryon-baryon interactions and to investigate the natureof the repulsive core which has not been understood yet.

In order to overcome the experimental difficulties in measuring low-energy hyperonproton scattering, we will use a new experimental technique, where a liquid H2 targetis used as hyperon production and hyperon scattering targets and a detector systemsurrounding the LH2 target detects a scattered proton and a decay product from ahyperon. The hyperon scattering event is kinematically identified. Because imagingdetectors used in past experiments are not employed, high intensity π beam can beused, allowing us to take high statistics data of 100 times more than the previousexperiments.

The experiment is performed at the K1.8 beam line by utilizing the K1.8 beam linespectrometer and the SKS spectrometer. A high intensity π beam of 2×107/spill at1.32 GeV/c is used to produce as many hyperon beam as possible. With 16×106 Σ−

beam and 55×106 Σ+ beam around 500 MeV/c which are tagged by the spectrometers,we will detect ∼10,000 Σ−p and Σ+p scattering events and ∼6,000 Σ−p → Λn inelasticreaction events in 60 days beam time in total.

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1 Introduction

It is one of the most important subjects to understand interactions between hadrons in a lowenergy region based on QCD in recent nuclear physics. Especially, the nuclear force betweentwo nucleons and interactions between baryons should be understood from this point ofview. The nuclear force has been studied extensively by pp and pn scatterings. The natureof the nuclear force is described well by one boson exchange model in a long range regionof more than 1 fm, while the nature for the short range region where two nucleons overlapis being tried to be understood theoretically. In this region, it is expected that quarks andgluons, the constituents of the nucleon, play an important role. In order to understand thenature of the nuclear force, it is crucially important to investigate the generalized baryonbaryon (B8B8) interaction including the hyperon nucleon (YN) and the hyperon hyperon(YY) sectors. The theoretical efforts of the B8B8 interactions have been developed by twodifferent types of theoretical model, one is the One boson exchange model such as NijmegenOBEP model and the other is quark based approaches such as Quark Cluster model and aLattice QCD simulation.

The Nijmegen group developed one boson exchange (OBE) models that extend nuclearforce to baryon-baryon interaction based on flavor SU(3) symmetry and the phenomenolog-ical core potential[1]. They developed two types of models with different descriptions of therepulsive core: one with a hard core and the other with a soft core.

Many efforts have been also devoted to understand the B8B8 interactions based on theQCD. A direct derivation of these interactions from QCD involves tremendous difficulties,such as the quark confinement and multi-gluon effects in the low energy phenomena. TheQuark Cluster model is developed as the effective models which take account of some im-portant QCD characteristics like the color degree of freedom, one-gluon exchange and so on.Kyoto-Niigata group developed the quark cluster model that describes the repulsive corefrom the quarks and gluons using the resonating group method[2, 3]. In the short rangeinteraction, B8B8 interaction is described by the color magnetic interaction and the quarkPauli effect and the nature of the repulsive core is naturally derived.

Recently, a new method to extract the B8B8 potentials in the coordinate space fromlattice QCD simulations has been proposed and applied to the NN system, and also to YNsystems. Fig. 1 shows the six independent B8B8 potentials for S-wave in the flavor SU(3)limit calculated by a lattice QCD simulation [5]. The newly appeared interactions are pre-dicted to show an interesting nature which is different from NN interaction especially in theshort range region. The (8s) component is completely Pauli forbidden for the most compact(0S)6 configuration, where all constituent quarks occupy the 0S state, and is characterizedby the strong repulsion originating from the quark Pauli principle. The the (10) state is al-most Pauli forbidden, the interaction is also strongly repulsive. On the other hand, the (8a)state turns out to have very weak interaction. The (1) component in the H-particle channelis attractive because of the color-magnetic interaction. The features of the calculated po-tentials completely agree with the Quark Cluster prediction. This agreement suggests thatthe quark Pauli blocking plays an essential role for the repulsive core in B8B8 systems asoriginally proposed in [2].

In order to investigate these interactions, the hyperon proton scattering experiment isthe most powerful way, because it enables us to study each interaction separately. As animportant feature of scattering experiments, it is also pointed out that the energy dependenceof the cross section is related to the shape of the potential. Table 1 shows the relationship

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Figure 1: The six independent B8B8 potentials for S-wave in the flavor SU(3) limit, extractedfrom the lattice QCD simulation at mπ =1014 MeV (red bars) and mπ =835 MeV (greenbars). [5]

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S B8B8(I) P = +1 (symmetric) P = −1 (antisymmetric)1E or 3O 3E or 1O

0 NN(I = 0) – (10∗)0 NN(I = 1) (27) –

ΛN 1√10

[(8s) + 3(27)] 1√2[−(8a) + (10∗)]

-1 ΣN(I = 1/2) 1√10

[3(8s) − (27)] 1√2[(8a) + (10∗)]

ΣN(I = 3/2) (27) (10)

Table 1: The relationship between the isospin basis and the flavor-SU(3) basis for the B8B8

systems. The heading P denotes the flavor-exchange symmetry, S the strangeness, and Ithe isospin.

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

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Figure 2: Theoretical predictions by the OBEP (Nijmegen Soft Core) models and the quarkcluster (RGM FSS) models for Σ+p and Σ−p elastic scatterings. The difference of thedifferential cross section of Σ+p channel is originated from a repulsive hard core due to thequark Pauli effect.

between the isospin basis and the flavor-SU(3) basis for the B8B8 interaction. In order tostudy the framework of B8B8 interaction and to investigate the nature of hard core, the ΣNinteraction plays an important role. The ΣN interaction is expected to be quite dependenton the configuration of the isospin and spin. Especially, the Σ+p channel is expected tobe very repulsive due to the (10) configuration which is almost Pauli forbidden state. Asshown in Table1, the Σ+p channel is simply described by two multiplets. The spin singletstate is described by the (27) configuration which is the same multiplet with NN(I = 1)interaction. The spin triplet state is represented by the (10) configuration which is expectedto be quite repulsive due to the almost Pauli forbidden state. Because the triplet statecontributes 3 times larger than the singlet state, the Σ+p interaction is directly related tothe Pauli forbidden state. In the Quark Cluster model, this repulsive force can be derivednaturally as the effect of quark Pauli effect. On the other hand, in the OBE model, suchlarge repulsive force is not obtained. This difference of the repulsive force appears as thedifference between the cross sections calculated by these theoretical models.

On the other hand, in the Σ−p channel, there is no large difference between these twomodels, although the Σ−p channel in (I = 1/2, S(spin) = 0) includes the (8s) configurationwhich is completely Pauli forbidden state. The contribution of boson exchange is expectedto be large from this theoretical calculation. Therefore the theoretical calculation has to

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reproduce the differential cross section of the Σ−p channel. The framework of the B8B8

interaction is developed based on the plenty data of NN scattering and the poor statisticsdata of Y N scattering as mentioned in the next section. Although the data of Y N scatteringis not sufficient, the data constraint to the theoretical framework which is applied to thevarious fields of the strangeness physics. The high statistics data of Σ−p elastic scatteringand Σ−p → Λn inelastic scattering is essential to test the consistency of the theoreticalframework extended to the SU(3) symmetry. When both theoretical models can reproducethe data of the Σ−p reactions and there is a difference in the Σ+p channel, the differencemight come from the quark contribution in the B8B8 interaction. Therefore it is essential tomeasure the scattering data of the Σ±p and Σ−p → Λn reactions to develop an understandingof the whole picture of the B8B8 interaction.

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Figure 3: Calculated NN and Y N total cross sections by QC models, fss2 (solid curves) andFSS (dashed curves), compared with the experimental data. This data is cited from [4].

1.1 Historical background of YN scattering experiment and the

ΣN interaction

In contrast to the abundant NN scattering data, the YN scattering data are very limitedas shown in Fig. 3 which shows the total cross sections and in Fig. 4 which shows thedifferential cross sections. The reason of this poor statistics is its short life time of thehyperons. Therefore imaging detectors which enable us to recognize the complicated reactiontopologies in a region of ∼cm were used. In the 1960’s, almost all experiments were performedwith bubble chambers. Because the bubble chambers required the low beam rates, stoppingK− method was the most efficient way to produce hyperons. Therefore the data of the bubblechamber were limited to the low momentum hyperon beam regions. The bubble chamber wassuitable detector for low energy hyperon scattering because it can be the hyperon productionand hyperon scattering targets and the low density of liquid hydrogen enables us to see along track of the scattered proton. However the bubble chamber was untriggerable detectorand could not also work under a high beam rate. Therefore the statistics is very limited.

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Figure 4: Calculated Σ+p and Σ−p differential cross sections by fss2 (solid curves) and FSS(dashed curves), compared with the experimental angular distributions. This data is citedfrom [4].

For the ΛN interaction, great progresses of the high resolution spectroscopy of Λ hyper-nuclei enable us to derive the spin dependent ΛN interactions from the level structure of theΛ hypernuclei [7]. On the other hand, other YN interactions are still not understood wellyet. For the ΣN interaction, the Σ±p scattering experiment were performed at the KEKPS in order to measure the differential cross section in the higher beam momentum region[8, 9, 10]. In this experiment, a scintillation fiber (SCIFI) active target, which is a trigger-able imaging detector, was used to recognize the scattering events. As shown in Fig. 5, theimage was efficiently taken with the trigger of the Σ hyperon production identified by themagnetic spectrometer. The experiment provided the differential cross sections of the Σ−pand Σ+p elastic scatterings in the higher momentum region of 0.4 < p(GeV/c) < 0.6 for thefirst time. However the statistics was again limited to ∼30 events and was insufficient totest the different theoretical models. The main reason was the limited π beam intensity of∼ 2×105/spill, because the image intensifier tube, the readout of the SCIFI target, was slowand the images of the different events overlapped in the high beam intensity. The carbonnuclei in the SCIFI target which consists of (CH)n also caused a background of the quasi-freescattering between the proton inside the carbon nucleus and the Σ beams. The quality ofthe scattering data is the same situation with the bubble chamber period.

The bound state of Σ hypernuclei was also searched for and only the 4ΣHe (T = 1/2, S = 0)

bound state was observed [12], and the heavier Σ hypernuclear data exhibited no bound state

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Figure 5: Typical image data, which wa identified as Σ+p elastic scattering for the twodifferent 2 dimensional plane, u − z plane ad v − z plane. This figure is cited from [9].

peaks, suggesting a large conversion width and a shallow or repulsive potential for the spin-isospin averaged Σ nuclear potential. A recent experiment at KEK measured quasi-free Σproduction spectra via the (π−, K+) reaction on medium and heavy nuclei [13]. The dataimply that the spin-isospin averaged Σ nuclear potential is strongly (> 30 MeV) repulsive[14,15]. However it is rather difficult to draw a quantitative conclusion on the interaction strengthfrom the Σ-nuclear continuum spectrum.

Therefore the high statistics scattering data of the Σp channels is quite disired.

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π

Κ+

Σ

p

π

LH2 targettracking detector

scattering angle

wire chamber

Calorimeter

Momentum analysed by SKS sectrometer

Momentum analysed by K1.8 sectrometer

measure trajectory and kinetic energy

Figure 6: Experimental idea for the YN scattering using a liquid hydrogen target and thesurrounding detectors. By measuring the Σ beam momentum and the momentum of thescattered proton, the kinematics of the Σp scattering is reconstructed with the informationof the Σ beam momentum, the scattering angle, and the energy of the scattered proton.

1.2 Experimental goal

We propose an experiment to measure the Σ−p and the Σ+p elastic scattering cross sectionsand the Σ−p → Λn reaction cross section with 100 times larger statistics than the previousexperiments. From the experience of the past experiments, the following points should beimproved.

• High rate meson beam should be handled to produce intense hyperon beam.

• Liquid hydrogen should be used as hyperon production target and hyperon-protonscattering target to be free from the unwanted background such as a quasi-free scat-tering.

• The quality of the data taking trigger should be sophisticated to select the hyperonproduction and the hyperon scattering event efficiently under the high intensity mesonbeam.

We propose a new experimental technique for the YN scattering, considering the abovepoints. Fig. 6 shows the conceptual experimental setup. We use a liquid hydrogen (LH2)target as a hyperon production target and hyperon-proton scattering target. The positiondetectors are placed surrounding the LH2 target to detect the scattered proton and the decayproduct from hyperon. For the scattered proton, the trajectory and the kinetic energy aremeasured by the detectors surrounding the LH2 target. Because the momentum vector ofthe Σ beam can be tagged by the beam line and the forward spectrometers, the scatteringangle can be obtained by the angle defined by Σ− beam and scattered proton. These threemeasurements, which are the Σ beam momentum, the scattering angle, and the energy of

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E251 data (0.3<p(GeV/c)<0.6)

450MeV/c NSC97a

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Figure 7: Simulated differential cross section of the Σ+p scattering in the momentum rangeof 0.5 < p(GeV/c) < 0.6 for the 55 × 106 tagged Σ+ beam. The black close circle and opencircle represent the simulation results for the pπ0 and nπ+ modes, respectively. The bluecircle and the read square represents the previous results from the KEK-E289 and KEK-E251 experiments[9], respectively. Theoretical predictions by the OBEP (Nijmegen SoftCore) models and the quark cluster (RGM FSS) models are shown.

the scattered proton, and the use of the LH2 target enable us to identify the scattering event,because the reaction is two body reaction and is kinematically determined.

Because the detector to identify the scattering event is not be irradiated to the beam,high intensity beam can be used. On the other hand, the difficulty of this technique isto distinguish the scattered proton from other protons such as from the hyperon decay.Other background source is the proton scattered by the hyperon decay products. Table 2summarized the background reactions. The strategy of the experiment is as follow. Becausethe decay channel of the Σ− is only π−n channel and there is no decay channel to proton, wewill first perform a Σ−p scattering experiment and establish the experimental method. Thenwe apply this method to Σ+p scattering experiment where there are much larger backgrounddue to the Σ → π0p decay. In order to remove such background, at least two particles, thescattered proton and the π+ or proton from the Σ+ decay, should be detected.

The expected results studied by the simulation are shown in Fig. 7, 8 and 9 for the Σ+p,Σ−p and Σ−p → Λn reactions, respectively, with the previous experimental data and thetwo theoretical calculations, the Nijmegen model and the Quark Cluster model.

For the Σ+p scattering, the Quark Cluster model predicts a larger cross section than theOBEP model due to the difference of the treatment of the hard core as shown in Fig. 7.The aim of the Σ+p channel is to provide a sufficient cross section data for the confirmaionof the effect of the hard core originating from quark Pauli effect which appears as thedifference of the differential cross section. The simulated differential cross sections, whichare derived separately for the different decay modes of Σ+, are obtained from ∼2,000 and∼3,000 scattering events in the momentum region of 0.5 < p(GeV/c) < 0.6 for the pπ0 andnπ+ modes, respectively. The assumed cross section for the simulation is 30 mb with a flat

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Figure 8: Simulated differential cross section of the Σ−p scattering in the momentum rangeof 0.45 < p(GeV/c) < 0.55 for the 16×106 tagged Σ− beam. The black close circle representsthe simulation results. The blue circle represents the previous results from the KEK-E289experiments [8]. Theoretical predictions by the OBEP (Nijmegen Soft Core) models and thequark cluster (RGM FSS) models are shown.

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Figure 9: Simulated differential cross section of the Σ−p → Λn inelastic scattering in thebeam momentum regions of 0.45 < p (GeV/c) < 0.55 with the theoretical predictions by theOBEP (Nijmegen Soft Core) models and by the quark cluster (RGM FSS) model.

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Figure 10: First estimation of the hard core radius of the nuclear force by R. Jastrow [16].The differential cross section of pp scattering at 90o are shown with theoretical predictionswith different core radius assumption.

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angular distribution. The reproduced distribution shows the flat distribution, although thereis fluctuations. The proposed experiment enable us to discriminate the theoretical modelsand to give information about the nature of the hard core.

The two theoretical calculations show similar behaviour in the Σ−p elastic scattering andthe Σ−p → Λn inelastic scattering as shown in Fig. 8 and 9. In these channels, we aimto measure the angular dependence of the differential cross section with enough statisticsand accuracy to test the framework of theoretical models. The simulated spectra shown inFig. 8 and 9 are obtained from ∼5,000 and ∼4,000 scattering events, respectively, in themomentum region of 0.45 < p(GeV/c) < 0.55. This data quality enables us to compare theangular dependence of the differential cross section with the theoretical models and checkthe theoretical framework for the first time. If theoretical models can reproduce the Σ−pdata and there is a difference in the Σ+p channel, the difference might come from the quarkcontribution in the B8B8 interaction.

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As an important feature of scattering experiments, it is pointed out that the energydependence of the cross section is related to the shape of the potential. Especially, in orderto investigate the hard core, the differential cross section of the S-wave has an essentialinformation. In the partial wave analysis, the differential cross section is described by thefollowing equation,

dσ

dΩ=

1

k2

∣∣∣∞∑

l=0

(2l + 1)eiδl sin δlPl(cos θ)∣∣∣2. (1)

Because Pl(0) is 0 for odd l, the S-wave contribution is large for the differential crosssection at θ = 90o. For the NN interaction, the hard core radius was estimated from theenergy dependence of the differential cross section at θ = 90o by R. Jastrow before theprecise partial wave analysis as shown in Fig. 10 [16]. The differential cross section datawere compared with calculations in which the repulsion core was represented by a hardsphere, using radii of 0.5 and 0.6×10−13 cm. The YN interaction is the same situation withthe Fig. 10 and the precise partial wave analysis is still difficult by the proposed experiment.However, the energy dependence provides quite important information and the value atθ = 90o is directory connected to the phase shift δ0. Fig. 11 shows a sensitivity for theenergy dependence of the differential cross section at θ = 90o in the proposed experiment.In the proposed experiment, the energy is still limited around 80 < Ekin(MeV ) < 170.For the low energy region, the bubble chamber data can be referred. For the high energyregion, by changing the detection angle of the K+ where we need the different experimentalsetup, the higher energy region can be obtained. By accumulating the energy dependentdata, experimentally we can provide the information about the hard core and the proposedexperiment is the 1st step for this purpose.

In this proposal, we present not only the experimental method but also the detailedanalysis of the simulation to verify the feasibility of the proposed experiment.

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Σ−p channelΣ−p elastic scattering Σ−p → Σ−”p”

Σ− → π−nΣ−p → Λn inelastic scattering Σ−p → Λn

Λ → π−”p”Σ−p → Σ0n inelastic scattering Σ−p → Σ0n

Σ0 → Λγ, Λ → π−”p”Scattering with Σ− decay product

np scattering Σ− → π−nnp → n”p”

π−p elastic scattering Σ− → π−nπ−p → π−”p”

Σ+p channelΣ+p elastic scattering Σ+p → Σ+”p”

Σ+ → π+n or Σ+ → π0”p”Σ+ decay Σ+ → π0”p”

Scattering with Σ+ decay productpp scattering Σ+ → π0p

pp →“p””p”np scattering Σ+ → π−n

np → n”p”π+p elastic scattering Σ+ → π+n

π+p → π+”p”

Table 2: Summary of the background of the Σp scattering. The main background is theproton scattered by the decay products of Σ. In the Σ+p scattering, the proton from the Σ+

also causes a large background.

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2 Yield estimation and beam time request

Before describing the details of experiment and analysis method, we present the beam timerequest and the exprimental conditions. Based on this beam time, we performed simulationstudies described in the later sections.

The requested beam time is summarized in Table 3. The beam time is planned based onthe experimental conditions summarized in Table 4. We request 16 × 106 tagged Σ− beamand 55×106 tagged Σ+ beam to detect ∼10,000 scattering events. It takes ∼ 20 day’s beamtime for each beam to accumulate the number of Σ beams, assuming that 2 × 107/spill πbeam is used. Here the spill is the 2 sec of flat-top in the 6 sec time period. In addition to thedata taking, we request a tuning time of 5 days which includes the beam tuning, operationcheck of the K1.8 and SKS systems, and the newly installed detector systems. We alsostudy the trigger rate by the SKS with and without the fiber system. As a calibration data,pp scattering or πp scattering is also taken to measure the systematics of our experimentalmethod.

At first, we will perform the Σ−p scattering experiment, because in this reaction thebackground level is much smaller. This channel is suitable to check the feasibility of thismethod. We will analyse the data of the Σ−p channel and prove the experimental feasibility.After this check, the Σ+p scattering should be carried out.

Σ−p scattering experimentDetector tuning and trigger study 5 days

Data taking of Σ−p scattering 24 daysCalibration data taking 3 days

Σ+p scattering experimentDetector tuning and trigger study 5 days

Data taking of Σ−p scattering 20 daysCalibration data taking 3 days

Table 3: Beam time request for each scattering experiment.

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Σ−p scatteringΣ− production cross section 245 μb

π− beam intensity 2 × 107/spill (2sec beam time in 6 sec cycle )LH2 target thickness 30 cmAcceptance of SKS 4.5%Survival rate of K+ 34%

DAQ live time 70%Analysis efficiency 70%Tagged Σ−/spill 45/spillTagged Σ−/day 6.6 × 105/day

Accumulated Tagged Σ− 16 × 106 (24 days)Σ−p scattering cross section 30 mb (assumption)Σ−p scattering probability 0.22%

Detection efficiency of scattered proton 35%Σ−p detection number 11,800

Σ+p scatteringΣ+ production cross section 523 μb

π+ beam intensity 2 × 107/spill (2sec beam time in 6 sec cycle )LH2 target thickness 30 cmAcceptance of SKS 7.0%Survival rate of K+ 40%

DAQ live time 70%Analysis efficiency 70%Tagged Σ+/spill 183/spillTagged Σ+/day 2.6 × 106/day

Accumulated Tagged Σ+ 55 × 106 (20 days)Σ+p scattering cross section 30 mb (assumption)Σ+p scattering probability 0.12%

Detection efficiency of two p’s (Σ+ → pπ0) 13%Detection efficiency of p and π+ (Σ+ → nπ+) 21%

Σ+p detection number (pπ0 decay mode) 4,400Σ+p detection number (nπ+ decay mode) 7,000

Table 4: Yield estimation of the Σ−p scattering and the Σ+p scattering..

17

3 Experimental setup

We propose an experiment to measure Σ±p scattering cross sections utilizing the SKS spec-trometer and the K1.8 beam line spectrometer at the K1.8 beam line. In addition to thenormal K1.8 experimental setup, we newly install a special detector system which are a liquidhydrogen target and surrounding detector of fiber tracker, drift chamber and calorimeters inorder to detect the scattered proton and the charged particles from hypron decay.

3.1 Magnetic spectrometers to tag Σ beams

In order to identify π±p → K+Σ± reactions and to measure the Σ hyperon beams, theSKS spectrometer and the K1.8 beam line spectrometer are utilized. Figure 13 shows theexperimental setup of the K1.8 beam line and the SKS spectrometers. We use the π− beam of1.325 GeV/c for the Σ− production and the π+ beam of 1.419 GeV/c for the Σ+ production,respectively. Figure 12 shows the differential cross section for the Σ± productions with thesereactions [17, 18]. The production cross sections with the π beams are ∼5 times smallerthan that with K− beam [19]. However, we select π beams for the following reasons. The(K−, π−) reaction suffers from the background of the K− decay. On the other hand, the(π, K+) reaction can identify the Σ production without any background. When the forwardscattered K+ is detected by the forward spectrometer, the momentum of the Σ hyperonsproduced by the πp → K+Σ reaction is larger than 400 MeV/c. If the scattered π fromthe K−p → πΣ reaction is detected by the forward spectrometer, the momentum of thehyperons is ∼ 200 MeV/c and the hypron decays immediately. In these viewpoints, weshould establish the experimental method using the π beams at first.

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

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Figure 12: Differential cross sections of the π±p → K+Σ± reactions. The left and rightfigures show the Σ− production using the 1.325.GeV/c π− beam [17] and the Σ+ productionusing the 1.419.GeV/c π+ beam [17], respectively. The θ represents the angle of the scatteredK+ in the center of mass system.

In order to obtain intense Σ beams, the intensity of the incident π beam is required tobe 107 Hz, which corresponds to 2 × 107/spill in 2 sec extraction time during 6 sec cycle.The spill structure of the slow extraction has a spike structure where very intense beamcomes instantaneously. The present beam rate is determined by this beam structure. At theK1.8 beam line, two MPWC’s (BC1,2) and two MWDC’s (BC3,4) are installed upstreamand downstream of the beam line spectrometer magnet, respectively. These chambers areoriginally designed to work at 107 Hz beam rate. However it is difficult to operate these

18

SKS Magnet

SDC3

SDC4

TOFLC

AC1,2

Κ+

SDC1SDC2

LH2 target +

Scattering detector

πp

BC1,2

BC3,4

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BH1

GC

Figure 13: Experimental setup of the K1.8 beam line. The K1.8 spectrometer and the SKSspectrometer analyze the incident π beam particle and the scattered K+, respectively.

chambers in the designed beam rate due to the instantaneous high intensity of beam. Inthese situation, in order to handle the high intensity π beam, the fiber tracker will be used,which is stable for the high intensity beam and has a better time resolution of the orderof 1 nsec. This better time resolution enables us to separate the real beam particle, whichinteract at the target, from the accidental beam. The incident π beam particles are definedby the two beam hodoscopes (BH1,2) placed about 11 m apart. The electron contaminationis rejected by gas cherenkov counter placed upstream of the BH1. The momenta of theincident π beam particles are analyzed by the K1.8 beam line spectrometer which consists ofQQDQQ magnet system and beam line fiber trackers. The original momentum resolution ofthe K1.8 beam line spectrometer is 0.014 % in rms. The usage of the fiber trackers makes theresolution worse due to the multiple scattering. However, the resolution is well acceptablefor the proposed experiment.

The readout system of the fiber tracker will be the same technology with the fiber vertextracker which is described the next subsection. The PPD (MPPC) and the special readoutboard using an ASIC (SPIROC-A) for PPD are used.

Scattered K+’s are detected with the SKS spectrometer. The magnetic field is set to2.1 T for the π−p → K+Σ− reaction with 1.3 GeV/c π− beam. For the Σ+ production via

19

h50Entries 155941Mean 1.201RMS 0.003021

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Figure 14: Left-Top: Expected missing mass spectrum of Σ−. Right-Top: Angular distri-bution of the scattered K+. Left-Down: Σ− momentum distribution. Right-Down: K+

momentum distribution.

the π+p → K+Σ+ reaction, we use 1.4 GeV/c π+ beam. Therefore the magnetic field isincreased up to 2.4 T. The momentum of each outgoing particle is analyzed with four driftchambers (SDC1,2,3,4) located upstream and downstream of the SKS magnet. For particleidentification, trigger counters (TOF, AC1·2, LC) are placed downstream of SDC4. For theidentification of K+, hits of TOF and LC and veto of AC are required.

The purpose of the spectrometers is to tag Σ beams as many as possible with a goodmomentum and angular resolutions. The usage of the high intensity beam will cause multitrack event for the beam and scattered particles. However the combination of these multitracks can be solved so as to have the Σ particle mass. Fig. 14 shows the expected missingmass of Σ− and the kinematical values for the πp → K+Σ reactions. The acceptances ofthe SKS for the Σ− and Σ+ reactions are 4.5% and 7.0%,respectively, taking into accountthe target positon in the present experiment. Here the angular distribution of the K+ ofthe Figure 12 is taken into account. The momenta of the scattered K+ are ∼0.8 GeV/c and∼0.97 GeV/c for the Σ− and Σ+ productions, respectively. Because the distance between thetarget and LC wall is ∼7.2 m, the survival rates of the K+’s are 34 % and 41 %, respectively.

The Σ− beam momentum has a peak at 0.49 GeV/c and ranges from 0.45 to 0.7 GeV/cas shown in Fig. 14. For the Σ+, beam momentum has a peak at 0.45 GeV/c and rangesfrom 0.42 to 0.65 GeV/c.

3.1.1 Performance of the spectrometer

The Σ− beam is identified from the missing mass of the π−p → K+X reaction. In thissimulation, we assumed that the position resolutions of chambers are 200 μm. The left-up

20

h1Entries 2594Mean -0.0001125RMS 0.003774

/ ndf 2χ 214.2 / 77Constant 3.9± 126.5 Mean 6.154e-05± -6.046e-06 Sigma 0.000070± 0.002998

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/ ndf 2χ 214.2 / 77Constant 3.9± 126.5 Mean 6.154e-05± -6.046e-06 Sigma 0.000070± 0.002998

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h2Entries 2594Mean 2.99e-05RMS 0.003652

/ ndf 2χ 232 / 74Constant 4.1± 131.1 Mean 5.949e-05± 2.718e-05 Sigma 0.000067± 0.002867

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/ ndf 2χ 232 / 74Constant 4.1± 131.1 Mean 5.949e-05± 2.718e-05 Sigma 0.000067± 0.002867

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Vertical angular resolution


/ ndf 2χ 65.99 / 47Constant 6.8± 271.5 Mean 3.07e-05± 5.27e-05 Sigma 0.000025± 0.001586

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Vertical angular resolution

Figure 15: Angular resolution of the SKS (left) and beamline spectrometer (right) at thetarget. The top figures and down figures show the horizontal and vertical scattering anglerresolution, respectively.

figure in Fig. 14 shows the missing mass spectrum of the π−p → K+X reaction whichshows the clear peak of Σ−. Because there is no background reaction, the Σ− can be clearlyidentified. The width of the peak is estimated to be 3.5 MeV (FWHM).

The momentum of the Σ− beam should be calculated from the momenta of π− beamand scattered K+ and the scattering angle between them. The momentum resolution of theK+ is expected to be 3 MeV/c which corresponds to Δp/p = 3.8 × 10−3. The momentumresolution of π− is expected to be one order better. Fig. 15 shows the angular resolutionof the SKS and beamline spectrometers at the vertex position. From the simulation, thescattering angle of the K+ is reconstructed with the resolution of 0.18 degree.

Momentum of a Σ− beam is reconstructed from the momenta of π− beam and K+ and thescattering angle. Fig.16 shows the momentum and angular resolutions of the reconstructedΣ− beam which are obtained to be σ=6.13 MeV/c and σ = 0.37 degree, respectively.

3.1.2 The (π, K) trigger rate

The (π, K) trigger is made as

PIin × Kout = (BH1 × BH2 × GC) × (TOF × AC × LC). (2)


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/ ndf 2χ 93.43 / 17Constant 13.2± 925.9 Mean 0.0046± 0.2437 Sigma 0.0040± 0.3728

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= 0.37 (degree)σ

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Figure 16: Momentum resolution and angular resolution of a hyperon beam.

21

Reaction Beam intensity (π, K) trigger rateΣ− production 106/spill 145/spillΣ+ production 4.3 × 105/spill 120/spill

For the present experimentReaction Beam intensity (π, K) trigger rate Real Σ production rate

Σ− production 2 × 107/spill 2900/spill 93/spillΣ+ production 2 × 107/spill 4800/spill 370/spill

Table 5: Summary of the (π, K) trigger rate obtained from the E19 experiment and theexpected trigger rate for the proposed experiment. The (π, K) trigger rate is just multipliedby the gain of the target thickness and beam intensity. The estimated numbers of the realΣ± productions are also included.

In the E19 experiment, the Σ± events were taken using the π±p → K+Σ± reactions with1.37 GeV/c π± beams as the calibration data. We can refer the trigger rate in the E19beamtime. The length of the LH2 target was 13.5 cm which is almost half length of thepresent experiment. The beam rates were 106 π−/spill and 4.3 × 105 π+/spill, respectively.Table 5 shows the summary obtained from the E19 experiment and the expected triggerrate for the proposed experiment. The (π, K) trigger rate is just multiplied by the gain ofthe target thickness and beam intensity. In the table, the estimated numbers of the realΣ± productions are also shown, which indicates that trigger rate is more than 20 timeshigher than the real Σ production. It is essential to make effective trigger considering theacceptable DAQ rate of ∼500/spill. If needed, the fiber vertex trackers information, whichwill be described in the next subsection, is also used to identify the additional particle fromthe target region.

3.2 Detector system to identify the Σp scattering

Figure 17 shows a schematic view of the LH2 target and surrounding detector system. Weuse a 30 cm long LH2 target as hyperon production and hyperon proton scattering targets.The diameter of the target is considered to be 4∼6 cm, because hyperon can not run insidethe LH2 target for a long range due to its short life time. Therefore it should be comparablewith the mean path length in the hyperon beam.

The LH2 target is surrounded by a scintillation fiber tracker made from 4 layer of scin-tillation fiber sheet, a cylindrical drift chamber and calorimeters in order to measure thetrajectories of the scattered proton and the decay products from hyperon. The energy of theproton can be measured by the calorimeter.

3.2.1 Fiber tracker for vertex reconstruction and trigger

For the high statistics hyperon proton scattering, it is essential to use high intensity π orK− beams to produce enough hyperon beams. In this situation, the ability to separate thereal scattering events from the accidental coincidence events is necessary. Because we donot use an imaging detector, the accidental coincidence events with the Σ production might

22

p

n

Σ −π−

Fiber tracker

LH2 target

Calorimeter

Tracking chamber

Κ + π−

280mm

100mm

580mm

Figure 17: Schematic view of the LH2 and surrounding detector system. The LH2 target issurrounded by 4 layers of fiber tracker, cylindrical drift chamber and calorimeter.

cause some errors to derive the cross section. Good time resolution of ∼1 ns to separate theaccidental events is required. Therefore we will install a fiber tracker at the most inner part,which also works as a vertex tracking system. The ability to trigger the scattering events isalso essential for high statistics experiment. Using the difference of the energy deposit in thefibers of π and proton, proton events can be selected on the trigger level. The fiber trackeris a three dimensional tracking detector. The 1st, 3rd layers, and 2nd, 4th layers have a uand v configuration, respectively. The cross section of the fiber is 0.5 × 1 mm2 and the totalreadout channel is ∼1500. The each fiber is read by PPD (MPPC) with a special readoutboard of MPPC, SPIROC, which enables us to read 32 ch of MPPC serially.

The SPIROC chip is an ASIC dedicated for the multi-channel PPD readout. The diagramof SPIROC board is shown in Fig. . The SPIROC chip has 32 channel inputs of PPD andeach channel has a preamplifier, slow shaper for an energy measurement, and fast shaperand discriminator for a time measurement [20]. The each discriminator output signal istransferred to a FPGA, then time information is obtained with a few ns resolution. Bysetting the threshold to the energy deposit of protons, these logic signals can also be usedas a trigger.

3.2.2 Calorimeter system

The calorimeter measures the total energy of a scattered proton. We consider a plasticscintillator for the calorimeter. In order to identify the hyperon proton scattering event, themeasured energy is compared with the calculated energy from the hyperon beam momentumand the scattering angle of the proton. The resolution of the calculated energy, which isdetermined by the angular resolution of the scattered proton, is σ = 3 MeV. The comparableresolution is required for the calorimeter.

23

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Figure 18: Diagram of the SPIROC board. The SPIROC chip has 32 channel inputs ofPPD and has a preamplifier, slow shaper for an energy measurement, and fast shaper anddiscriminator for a time measurement. The each discriminator output signal is transferredto FPGA, then time information is obtained with a few ns resolution. The multiplexedanalogue output is sent to external ADC chip and the digitized ADC data are sent serially.

3.2.3 Expected performance of detector system surrounding the LH2 target

• Acceptance for scattered protons

Fig. 19 shows the scattering angle distribution of Σ−. Events where the Σ− is scatteredto the forward angle can not be detected, because the energy of the corresponding protonis quite small and such proton cannot escape proton target or stops at the inner fibers. Fig.20 shows the momentum and energy distributions of the scattered proton. The hatchedspectrum shows the detected events. The energy threshold of proton is ∼30 MeV. For thescattering events with a larger scattering angle around 180 degree, the proton is scatteredto the forward region where the detector system has a small acceptance. The fraction ofaccepted and generated events is estimated to be ∼0.35.


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Figure 19: Scattering angle distribution of Σ− at the center of mass system. The hatchedspectrum shows the events which are detected by the detector.

• Angular resolution and reconstructed energy resolution of proton

24


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Figure 20: Momentum and kinetic energy distribution of scattered protons. The hatchedspectrum shows the accepted events. The energy threshold of the kinetic energy is ∼20 MeV.

The scattering angle of the proton is calculated using the hyperon beam track determinedfrom spectrometer and the proton track. Because the elastic scattering event is identified bychecking the consistency between scattering angle and energy, the good angular resolutionis required to make the S/N ratio be better. Fig. 21 shows the angular resolution of thescattering angle. In the simulation, we assumed that the chamber has 3 u v planes and thefiber tracker has 2 layers of u v planes. The fiber width of 1 mm is also taken into account.The typical angular resolution is 1.3 degree which is determined by the multiple scattering inthe materials such as a target vessel, a vacuum window and fibers and so on. The resolutionof the reconstructed energy of the scattered proton is estimated to be σ =3.2 MeV as shownin Fig. 22.

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25

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Figure 22: Momentum and kinetic energy resolution for scattered proton.

• Vertex resolution of scattering point

The vertex point of scattering point is calculated as the closest distance point betweentracks of hyperon beam and scattered proton. The Fig. 23 shows the vertex distributionsand the closest distance between these two tracks. The vertex resolution of z and x,y arecalculated to be 2.0 mm and 1.0 mm, respectively, as shown in Fig. 24.

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Figure 23: Vertex distribution of Σ−p scattering point and closest distance distribution.

26

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Figure 24: Resolution of Σ−p scattering vertex.

• Particle identification of scattering particle

For the Σ− production event, π− from Σ− decay and proton from some interactions aredetected by the detector around the target. Therefore the scattered proton and π− should beidentified. We are trying to separate these particles using ΔE per unit length at fibers andtotal energy deposit at the calorimeter, ΔE-E method. Fig. 25 shows the relation betweentotal energy deposit per unit length at 4 fibers and the energy deposit at the calorimeter,where the red and green points represent proton and π−, respectively. In this plot, theenergy resolution is not considered yet. There might be a contamination of the π at the highenergy proton region. In order to separate π and proton without any contamination, we useother information such as the β measurement between a start counter and the calorimeter.

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Figure 25: Relation between total ΔE per unit length at all fibers and E at the calorimeter.The red and green points represent proton and π−, respectively.

27

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Figure 26: The background events of the Σ−p scattering. The main background is np andπ−p scattering after the Σ− decay. The Σ−p → Λn conversion process is identified and it isone of our measurement. However The Σ−p → Σ0n conversion process can not be identified,and it makes background events.

4 Background events

We detect the scattered proton with a coincidence of the Σ production. However there arebackground events due to the decay product of Σ hyperons. At first, in the Σ+ case, themain background is the proton from the Σ+ → π0p decay. Other background sources areprotons which are scattered by the decay products from the Σ decay such as proton, neutron,and π±. For the Σ−p reaction, the conversion processes such as Σ−p → Λn and Σ−p → Σ0nreactions become backgrounds for the Σ−p elastic scattering, although Σ−p → Λn is one ofthe interesting channel. Fig. 26 and Fig. 27 show the summaries of the background reactionsfor the Σ−p reaction and the Σ+p reaction. In order to estimate these background levels,we performed a simulation considering the realistic cross sections and angular distributionsof these background events as described below. The background cross sections are quitedependent for the momentum regions of the neutron, proton and π±. Fig. 28 and Fig. 29shows the momentum and kinetic energy distributions of neutron and π− from Σ− decay.Therefore in the simulation, energy depndent cross sections are also taken into account. Inthis section, we describe the background level and method to identify the Σp scatteringevents and also to suppress background events.

4.1 Neutron proton and proton proton scatterings

In order to estimate the contribution from np scatterings, the realistic cross section andangular dependence should be used. We used theoretical calculation of np scattering by

28

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p (scat)

p (scat)

p (decay)

π0 π +

n

Σ+

p (scat)

π +

n

Σ p scattering

Σ decay

Background (scattering with decay products)

+

+

Figure 27: The background events of the Σ+p scattering. Because there is a pπ0 decaychannel, the proton from Σ+ decay makes background in addition to the scattering with thedecay products.


Momentum (GeV/c)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

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3000

3500


Momentum of neutron h11Entries 115237Mean 111.6RMS 53.27

(MeV)KinE0 50 100 150 200 250 300 350 400

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of neutronKinE


Momentum (GeV/c)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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Momentum of neutron (scat) h12Entries 185523Mean 84.43RMS 52.69

(MeV)KinE0 50 100 150 200 250 300 350 400

0

1000

2000

3000

4000

5000

6000

7000

8000

9000


of neutron (scat)KinE

Figure 28: Momentum and kinetic energydistributions of the neutron from Σ− decay.The bottom figures are the same distribu-tions where neutron and proton scatteringoccurs. The hatched histogram shows theevents where scattered proton is detected bythe surrounding detector.


Momentum (GeV/c)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5000

10000

15000

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-πMomentum of h11Entries 285733Mean 133.7RMS 50.98

(MeV)KinE0 50 100 150 200 250 300 350 400

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-π of KinE


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(scat)-πMomentum of h12Entries 15027Mean 155RMS 42.53

(MeV)KinE0 50 100 150 200 250 300 350 400

0

100

200

300

400

500

600

700

800

h12Entries 15027Mean 155RMS 42.53

(scat)-π of KinE

Figure 29: Momentum and kinetic energydistributions of the π− from Σ− decay. Thebottom figures are the same distributionswhere π− and proton scattering occurs. Thehatched histogram shows the events wherescattered proton is detected by the surround-ing detector.

29

fss2 model by Fujiwara et al. as shown in Fig. 30 [4]. For the pp scattering, we refereedthe experimental data. It is remarking that the cross sections increase when the energies ofneutron and proton become small. In the bottom figures of Fig. 28, the kinematic energydistribution of neutron which interacts proton is shown. Although number of emitted neutronfrom Σ decay decreases in low energy region, the number of scattered neutron increases dueto the increase of the total cross section.

In the Monte Carlo simulation, both of the total cross section and differential cross sectionare taken into account.

Kinetic energy (MeV)0 50 100 150 200 250 300

Cro

ss s

ecti

on

(m

b)

210

310 pp scatteringnp scattering

np & pp total cross section

(degree)CMθ0 20 40 60 80 100 120 140 160 180

Dif

fere

nti

al c

ross

sec

tio

n (

mb

/sr)

0

5

10

15

20

25

50 MeV

100 MeV

150 MeV

200 MeV

300 MeV

np differential cross section

Figure 30: Total and differential cross section of np scattering by theoretical calculationbased on fss2 model.

4.2 π− proton and π+ proton scatterings

Fig. 31 shows the π−p total and elastic cross sections. The difference between total andelastic cross sections at the momentum region of 0.1 < p < 0.4 GeV/c is understood as thecontribution from a charge exchange reaction (π−p → π0n). Therefore we take only thecontribution of the π−p elastic scattering into account. As the angular distribution, we usea flat distribution in the CM system. Because the cross section of the π−p elastic scatteringis a rather small value of 20 mb, the background level of the π−p reaction is smaller thanthat of the np scattering.

Fig. 32 shows the π+p total and elastic cross sections. Compared with the π−p elasticscattering, the π+p scattering has a larger cross section of ∼200 mb which is comparablewith the pp scattering.

4.3 Background kinematics

In the event generator in a Monte Carlo simulation, we included the background processesdescribed in the previous subsection. In order to identify the Σp scattering, we check theconsistency between the hyperon beam momentum, the scattering angle and energy of thescattered proton. Here the scattering angle is defined by a crossing angle between theoutgoing proton track and hyperon beam as shown in Fig. 33. We also used the samescattering angle for the background events. Fig. 34 shows the scattering plots between thescattering angle and the momentum of proton. For the Σ−p elastic scattering event, thereis a reasonable correlation between the angle and the momentum, while there are broad

30

Momentum (GeV/c)-110 1 10

Cro

ss s

ecti

on

(m

b)

1

10

210

p total-πp elastic-π

p total cross section-π

Figure 31: π−p total cross section and elasticcross section.

Momentum (GeV/c)-110 1 10

Cro

ss s

ecti

on

(m

b)

10

210

p total+π

p elastic+π

p total cross section+π

Figure 32: π+p total cross section and elasticcross section.

distributions due to the background events. In the right figure (Σ+p channel) of Fig. 34,there is also a band of the Σ+ decay. Unfortunately, there are overlap region between them.Therefore good angular resolution and good energy resolution are important to separatethese backgrounds.

Here we define the following values,

• Emeasure : measured kinetic energy of the proton by the calorimeter,

• Ecalculate : calculated kinetic energy from the hyperon beam momentum and the scat-tering angle,

• ΔE : difference between Emeasure and Ecalculate, (ΔE = Emeasure − Ecalculate).

For the Σp scattering event, the ΔE should be zero, although the ΔE has a broad distributionfor the background events. Fig. 35 shows the ΔE distribution for the Σ− beam events.. Thepeak around ΔE = 0 MeV corresponds to the Σ−p elastic scattering events. There arebroad structures due to the background events. The total cross section of the Σ−p elasticscattering is assumed to be 30 mb. Because the cross sections of the background reactionsare also taken into account, the S/N ratio is reliable. The width of the peak is determinedby the resolution of the scattering angle.

31

πΚ+

Σ

p

π

scattering angle

Σp scattering

πΚ+

Σ

pπ

Calorimeter

n

Background

scattering angle

Figure 33: Definition of the scattering angle. The angle is defined as the crossing anglebetween the hyperon beam track and the outgoing proton.

(degree)θ0 20 40 60 80 100 120 140

Mo

men

tum

(G

eV/c

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p scattering-Σnp scattering

p scattering-πn conversionΛn conversion0Σ

0.475<p<0.525scatθ: scatMomentum

(degree)θ0 20 40 60 80 100 120 140

Mo

men

tum

(G

eV/c

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7p scattering+Σ

np and ppscattering

p scattering+π

decay+Σproton from

0.425<p<0.475scatθ: scatMomentum

Figure 34: Relation between the scattering angle and the momentum of the scattered protonfor the Σ−p event and background events. The scattering angle is defined by the cross angleby a hyperon beam track and a outgoing proton.

4.3.1 Background suppression

In the ΔE distribution of Fig. 35, there are large background below the Σ−p scatteringevent. Therefore the suppression of the background events is essential.

At first, we check the closest distance between the hyperon beam and the outgoing proton.Fig.36 shows the closest distance distribution. For the scattering event, this closest distanceconcentrates around zero as shown by the blue histogram in Fig.36, while in the backgroundevents, it shows a broad distribution. When the closest distance is reqired to be less than 5mm, ∼45 % of background events are suppressed and the survival ratio for the signal eventis 97%.

As second method to suppress more background, we detect and analyse a π− particlefrom the Σ− decay and reconstruct the np scattering background as explained in Fig. 37.The detector system around the LH2 target has a large acceptance of ∼79 % for π from theΣ− decay. By using the information of the π−, we try to suppress the background event dueto np scattering. When we obtain the momentum of the π−, the momentum of the neutronfrom the Σ decay can be obtained assuming the Σ decay kinematics. It is difficult to measure

32


E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

200

400

600

800

1000

1200

1400

1600

1800

2000


np scattering

p scattering.-π

n conversionΛ

n conversion0Σ

p scattering-ΣE for Δ

Figure 35: Deference between the calculated kinetic energy from the scattering angle andmeasured kinetic energy. The peak structure around ΔE=0 MeV corresponds to the Σ−pscattering. The green and yellow hatched spectra show the background due to the np andπ−p scatterings, respectively.


Distance (mm)0 5 10 15 20 25 30 35 400

2000

4000

6000

8000

10000

12000

14000


p scattering-Σ

np scattering

p scattering-π

p)-Σratio (<5) = 0.972 (

ratio (<5) = 0.569 (np)

p)-πratio (<5) = 0.570 (

Closest Distance (priVtx=p)

Figure 36: Closest distance distribution for each reaction. The number shows the survivalratio when we set cut value at 5 mm.

the kinetic energy of π−. However by measuring the trajectory of π−, the momentum canbe obtained using an assumption. The emission angle of the π− from the Σ− beam can beobtained using the Σ− beam direction and the direction of the π−. If we assume that the π−

comes from the Σ− decay, the momentum of the π− can be obtained using the momentum ofthe Σ− beam and the emission angle (θπ). Then the neutron momentum can be obtained by�p(n) = �p(Σ−) − �p(π−). The momentum of the neutron can be calculated with an accuracy

of 1.8 MeV/c.Next, we assume that outgoing proton is scattered by the neutron from the Σ− decay. We

check the consistency between the scattering angle (θnp) between the outgoing proton and the

33

π

Κ+

p

πCalorimeter

n

np scattering reconstruction

θπ

1. Assume that π comes from decay of Σ. Calculate θπ.2. Calculate |p(π)| from θπ. The p(π) can be obtained.3. Neutron momentum pn can be obtained from p(n) = p(Σ)−p(π).4. Assume that proton is scattered by the neutron from Σ decay.5. Calculate θnp from p(n) and p(p)6. Check the consistency of np scattering with E(p) and θnp.

θnpp(n)

p(π)

p(Σ)

p(p)

Figure 37: Reconstruction procedure of np scattering events.

neutron and kinetic energy of the proton. Fig.38 shows the difference between the measuredenergy of the proton and the calculated energy with the assumption of np scattering. Thenp scattering event shows the peak structure around ΔE = 0 MeV, although other reactionsshow broad distributions. If we reject events of -8 < ΔE < 8 (MeV), the np scatteringevents are suppressed to ∼70%, although about 10% of the Σ−p scattering is also removed.

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 100

10

210

310

p scattering-Σ

np scattering

p scattering.-π

n conversionΛ

n conversion0Σ

E for np scatteringΔ

p 6782/7958 (0.85)-Σn 5968/6012 (0.99)Λ

Figure 38: Difference between the measured energy of the proton and the calculated energywith the assumption that the proton is scattered by the neutron from the Σ− decay. The npscattering event shows the peak structure around ΔE = 0 MeV, although other reactionsshow broad distributions.

34

5 Analysis and the expected result

In this section, we present the expected results using the 16×106 tagged Σ− beam and the55×106 tagged Σ+ beam. The procedures to select the scattering events and to derive thecross sections are described in detail.

5.1 Event selections of Σ−p elastic scattering and Σ−p → Λn inelas-

tic scattering

In the Σ− experiment, there are five possible reactions where a proton is emitted with acoincidence of the Σ− production, as shown in Fig. 26, that is Σ−p elastic scattering, Λninelastic scattering, Σ0n inelastic scattering, np scattering and π−p scattering. In thesereactions, the Σ−p elastic scattering can be identified by detecting the scattered proton.By detecting the π− from the Σ− decay, the np scattering and Λn inelastic scattering canbe identified with some assumptions as explained in the previous section. The procedureto identify the Λn inelastic scattering is shown in Fig. 39, where the π− and proton areassumed to be the decay product of Λ.

πΚ+

pπ

Calorimeter

n Λ

Reconstruction of Σp Λn conversionΣ p Λn- 0. We know p(p) and direction of π.

1. Assume that p and π come from a decay of Λ. Measure the opening angle θpπ.2. Calculate |pπ| so that the invariant mass of π and p becomes Λ mass.3. Calculate p(Λ) by p(p) + p(π).4. Measure the scattering angle θΛ from p(Σ) and p(Λ).5. Check the consistency of Λn conversion with p(Λ) and θΛ.

θpπ

θΛ

p(Σ)

p(π) p(p)

p(Λ)

Figure 39: Reconstruction procedure of the Λn conversion process.

In the analysis, we make three ΔE (Δp for Λn reaction) distributions assuming thefollowing three reactions, Σ−p elastic scattering, Σ−p → Λn inelastic scattering and npscattering. The Fig. 40 shows the ΔE distributions for these three reactions. For eachassumption, there is a peak structure around ΔE = 0 which corresponds to the assumedreaction and a broad structure due to other reactions. In order to improve the S/N ratiofor the Σ−p and Λn reactions, the following cuts are applied.

• the closest distance cut as shown in Fig. 36 for Σ−p scattering. For Λn conversionevent, we check the closest distance between π− and proton.

• np scattering cut. The event of -8 < ΔEnp (MeV) < 8 is removed as the np scatteringevents. The survival ratios of Σ−p and Λn reactions are estimated to be ∼85% and∼99%, respectively.

35

• Λn conversion cut for Σ−p scattering event. The events of −0.05 < Δp (GeV/c) < 0.1are rejected as Λn conversion events.

• Σ−p scattering cut for Λn conversion event. The events of −10 < ΔE (MeV) < 10 arerejected as Σ−p scattering events.

Fig.41 shows the ΔE distribution after these background suppression cuts. It is remark-ing that the Λn scattering process is almost background free due to the Q value at the Λdecay. For the Σ−p scattering, although the S/N ratio is much improved, there exists theunavoidable background. When the differential cross section is derived, the contributionfrom the background should be subtracted.

The number of the Σ−p scattering events is estimated to be 9,500 for the 16×106 taggedΣ− beam assuming that the total cross section of the Σ−p scattering is 30 mb and theangular distribution is flat. The Λn conversion is expected to be 6,000 events with the sameassumption, that is the conversion cross section is 30 mb.

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

200

400

600

800

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1200

1400

1600

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2000 p scattering-Σ

np scattering

p scattering.-π

n conversionΛ

n conversion0Σ

p scattering-ΣE for Δ

p 11839/11994 (0.99)-Σ

n 10170/10613 (0.96)Λ

Momentum (GeV/c)Δ-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

200

400

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800

1000

1200

1400

1600 p scattering-Σ

np scattering

p scattering.-π

n conversionΛ

n conversion0Σ

n conversionΛ→p-Σp for Δ

p 7256/7981 (0.91)-Σn 6534/6652 (0.98)Λ

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 100

10

210

310

p scattering-Σ

np scattering

p scattering.-π

n conversionΛ

n conversion0Σ

E for np scatteringΔ

p 6782/7958 (0.85)-Σn 5968/6012 (0.99)Λ

Figure 40: ΔE distributions for Σ−p (Left-Up) and np scatterings (Right-Up) and Δp dis-tribution for Σ−p → Λn conversion reaction (Left-Down). For the Σ−p scattering event,ΔE distribution makes a peak around ΔE = 0, although other reactions makes the broaddistributions. This relation is the same for other reactions. It is remarking that the Λnconversion process is almost background free as shown in the Right-Up figure.

5.2 Event selection of Σ+p elastic scattering

The Σ+p scattering experiment is more challenging than the Σ−p scattering experiment dueto the following reasons. At first, the life time of the Σ+ is half than that of Σ− because

36


E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

200

400

600

800

1000

1200


np scattering

p scattering-π

n conversionΛ

n conversion0Σ

11994 (All event)

11271 (Cdist cut)

10238 (Np cut)

n cut)Λ9580 (

p scattering-ΣE for Δ h4Entries 38337Mean -0.09991RMS 0.1128

Momentum (GeV/c)Δ-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

100

200

300

400

500

600

700

800

900


np scattering

p scattering-π

p scattering-Σ

n conversion0Σ

6652 (All event)

6380 (Cdist cut)

6343 (Np cut)

p cut)-Σ6040 (

nΛ →p -ΣMomentum for Δ

Figure 41: ΔE distribution for the Σ−p reaction (Left) and Δp distribution for the Σ−p → Λnconversion reaction (Right) after the background suppression. The numbers in the his-tograms represent the survival event number after each cut.

there is two decay modes, Σ+ → pπ0 and Σ+ → nπ+. The scattering probability becomesabout half of the Σ−p scattering. The second point is the background level, which includesthe proton from the Σ+ decay, which does not exist in the Σ−p scattering, and also thescattering with the decay products. The background cross section of the π+ is also 10 timeslarger than the π−p cross section as shown in Fig.32.

Fig. 42 shows the ΔE distribution of the Σ+p scattering assumption. The left and rightfigures show the ΔE distributions for the Σ+ → pπ0 decay mode and the Σ+ → nπ+ decaymode, respectively. In the left figure of the Σ+ → pπ0 mode, the background distributiondue to the Σ+ decay is scaled to 1/100. Therefore, if we detect only one proton, almostall protons are from the Σ+ decay. In order to suppress the contribution of the Σ+ → pπ0

decay, It is indispensable to detect two particles, which are the scattered proton and othercharged particle from the Σ+.

In order to improve the S/N ratio, the following cuts are applied which is almost thesame technique used for the Σ−p scattering.

• Two-particle detection is required in order to suppress the Σ+ decay events. The two-proton detection probability is roughly 13% for the Σ+p scattering. For the nπ+ decaymode, the detection probability for the scattered proton and the π+ is about 22%.

• The closest distance cut between the Σ+ beam and the scattered proton. Fig. 43 showsthe closest distance distributions for two decay modes.

• The np scattering cut is also applied for the nπ+ decay mode. Fig. 44 shows the ΔEdistribution of the np scattering.

Fig. 45 shows the ΔE distribution after the above suppression cuts. In the pπ0 decaymode, by selecting two proton events, the background due to the decay can be removedalmost completely. Because, for the pp event, the energy of proton from the Σ+ decay isdivided by two protons, the probability to escape two proton from the target is small. Onthe other hand, in the Σ+p scattering events, the proton from the decay has a higher energythanks to the Q value at the decay. Therefore the two proton detection probability is ratherhigh and this makes the S/N ratio better. For the π+n decay mode, the np scattering can be

37

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

500

1000

1500

2000

2500

3000

3500

p scat+Σpp scat

decay (1/100)+Σ

)0πp→+Σ Total Energy Deposit Ecal-E0 (Δ

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

500

1000

1500

2000

2500

3000

3500

4000

4500

p scat+Σpp scat

p scat+π

)+πn→+Σ Total Energy Deposit Ecal-E0 (Δ

Figure 42: ΔE distributions for Σ+p scattering assumption. The left figure shows the ΔEdistribution for the Σ+ → pπ0 decay mode. The right figure shows the ΔE distributionfor the Σ+ → nπ+ decay mode. In the left figure of the Σ+ → pπ0 mode, the backgrounddistribution due to the Σ+ decay is scaled to 1/100. Therefore, if we detect only one proton,almost all protons are from the Σ+ decay. It is indispensable to detect two particles, whichare the scattered proton and other charged particle from the Σ+, in order to suppress thebackground from the Σ+ → pπ0 decay.

suppressed. However the π+p scattering events can not be suppressed in the present method,thus there still exists the background due to the π+p reaction.

5.3 Differential cross section

We calculate the differential cross section from the number of detected Σp scattering eventsand the track length of Σ beam in the LH2 target. The differential cross section is definedby the following equation,

dσ

dΩ(cosθ, p) =

Σi(Nscat,i(cosθ, p)/εi(cosθ, vertex))/εana

Lbeam(cosθ, p) · ρLH2 · dΩ. (3)

The εi is the efficiency to detect the i-th scattered proton. This depends on the scatteringangle and the scattering point. Therefore, this efficiency correction is applied event by event.

mm0 2 4 6 8 10 12 14 16 18 20

0

100

200

300

400

500

600

700

All sum

p scattering+Σ

pp scattering

p 4050/4373 (0.93)+Σ

np 6809/12633 (0.54)

Closest Distance

mm0 2 4 6 8 10 12 14 16 18 20

0

1000

2000

3000

4000

5000

6000

All sum

p scattering+Σ

np scattering

p scattering.+π

p 6513/6947 (0.94)+Σ

np 43142/75137 (0.57)

p 58645/102056 (0.57)+π

Closest Distance

Figure 43: The closest distance distribution between the Σ+ beam and the scattered protonfor the pπ0 decay mode (left) and nπ+ decay mode.

38

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 100

1

10

210

310

410

p scattering+Σ

np scattering

p scattering.+π

Kin np scattering EΔ

p 5850/6914 (0.85)+Σ

Figure 44: The ΔE distribution with assumption of the np scattering.

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

200

400

600

800

1000

4089 (All events)

3614 (Cdist cut)

p scattering+Σpp scattering

(0<cdist<4)Kin

p scattering EΣ Δ

E (MeV)Δ-100 -80 -60 -40 -20 0 20 40 60 80 1000

200

400

600

800

1000

1200

1400

1600

1800

6638 (All events)

5902 (Cdist cut)

5209 (np scat cut)

p scat+Σnp scat

p scat+π

(cdist && np scat cut)Kin

p scattering EΣ Δ

Figure 45: The ΔE distribution after the background suppression cut for the pπ0 decay mode(left) and the nπ+ decay mode (right). By selecting two proton events, the background dueto the decay can be removed almost completely. For the π+n decay mode, the np scatteringcan be suppressed. However the π+p scattering events can not be suppressed in the presentmethod, so there exists the background due to the π+p reaction.

39

cut Σ−p scattering Λn conversionClosest distance cut 0.94 0.96np scattering cut 0.91 0.99Λn conversion cut 0.94 –Σ−p scattering cut – 0.95

total 0.80 0.90

cut Σ+p scattering (pπ0 decay) Σ+p scattering (nπ+ decay)Closest distance cut 0.88 0.88np scattering cut – 0.88

total 0.88 0.77

Table 6: Summary of the each cut efficiency.

The Lbeam(cosθ, p) represents the track length considering the detector acceptance. Forexample, the scattering event, where the proton is scattered to forward angle with a largescattering angle (cosθ = −1), is out of the acceptance at the downstream of the LH2 target,because there is no detector coverage for such forward going proton as shown in Fig. 48.The Lbeam(cosθ, p) is the track length in the region of LH2 where a reasonable acceptance isobtained. The εana represents the efficiency of analysis cut such as proton detection cut andthe closest distant cut and so on.

5.4 Cut efficiencies

Table 6 shows the summary of the cut efficiencies.

5.5 Efficiency to detect the scattered proton

The efficiency of detecting the scattered proton depends on the reaction position, momentumof the proton and scattering angle. We estimate this efficiency event by event with a MonteCarlo simulation. Fig.46 shows schematic view of Σ−p scattering. The reaction point,scattering angle and momentum of proton can be obtained from the detector information.The azimuthal angle along the Σ− is a free parameter. In the simulation, we generate protonwith the detected momentum at the detected point. The direction of the proton is defined byθ and φ. As the θ, the obtained value is used. The φ is the free parameter and is generateduniformly from 0 to 360 degree. Then the efficiency is obtained as the ratio of detectedproton number and generated proton number (the generated number is 1000 for each event).

5.6 Σ track length considering the detector acceptance

Next, we obtain the track length of the Σ± beams in the LH2 target. We do not know thetrack length event by event, because the decay point of the Σ is not detected. However,because we measure the primary vertex point and the Σ beam momentum as the missingmomentum of the πp → K+X reaction, we can estimate the total track length using a MonteCarlo simulation using the measured information. Fig.47 shows the estimated flight lengthdistribution for three momentum regions.

40

Figure 46: Schematic view of Σ−p scattering.


mm0 20 40 60 80 100 120 140

1

10

210

310

410


Total Length = 2746495 (mm)

Total Length = 2036536 (mm) (0.45<p<0.55)

Total Length = 684460 (mm) (0.55<p<0.65)

Total Length = 23726 (mm) (0.65<p<0.85)

Target2

Flight Length in LH h2Entries 1e+07Mean 9.589RMS 9.45

mm0 10 20 30 40 50 60 70 80 90 100

1

10

210

310

410

510

h2Entries 1e+07Mean 9.589RMS 9.45Total Length = 5314866 (mm)

Total Length = 2989017 (mm) (0.4<p<0.5)

Total Length = 2129105 (mm) (0.5<p<0.6)

Total Length = 196732 (mm) (0.6<p<0.8)

Target2

Flight Length in LH

Figure 47: Estimated flight length distribution for three different momentum ranges by theMonte Carlo simulation using the information of the primary vertex and the momentumobtained from the spectrometer analysis. The sum of the flight length is the total tracklength which is written as “Total Length”.

We have to consider the detector acceptance as a function of the primary vertex point(z, beam direction). Fig.49 shows the primary vertex distribution for each scattering angle.The open and red hatched histograms show the generated scattering point and the detectedscattering point, respectively. For the forward going proton (cosθ ∼ −1), detection ratiodecreases at the downstream primary vertex region, because there is no detector acceptanceas shown in Fig.48. Therefore, if we use the same track length for all scattering angle range,the differential cross section at cosθ ∼ −1 might be underestimated. For each scatteringangle range, we set the acceptable primary vertex region where the detector acceptance isreasonable. Blue lines in Fig.49 show the cut points. When the differential cross sectionis derived, we use the total track length within the acceptable region for each cosθ region(Lbeam(cosθ, p)). In order to count the scattering number (Nscat,i(cosθ, p)), the primaryvertex point is required to be within the region.

41

Out of acceptance

pp

pp

Figure 48: Schematic view of the detector acceptance. The detector acceptance depends onthe primary vertex and scattering angle.

h11_0Entries 1415Mean -1.915RMS 82.23

Primary vertex z (mm)-150 -100 -50 0 50 100 1500

10

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30

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60


< -0.9CMθ-1.0 <= cos

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< -0.8CMθ-0.9 <= cos



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Figure 49: Primary vertex distribution for each scattering angle for the data of 0.45 <pΣ(GeV/c) < 0.55. The open histogram shows the generated distribution. The red histogramshows the primary vertex distribution when the proton scattered to the each angle is detected.For the back-scattering events around cosθCM = −1, the reaction point is limited to theupstream region of the target. For the forward scattering events around cosθCM = 1, thekinetic energy of the proton is small and such low energy proton can not be detected.

42

5.7 Background subtraction

In order to identify the Σp scattering event, we apply the kinematics cut to check the energydifference between measured proton energy and calculated proton energy. However, thereexists unremovable background as shown in Fig.41. We have to estimate the amount ofthe differential cross section and angular distribution due to the background. In order toestimate the background level and obtain the contribution of the real event, we make a plotof the double differential cross section d2σ/dΩdE for each scattering angle from the ΔEdistribution in Fig. 45. Fig. 50 shows the d2σ/dΩdE distribution for the Σ−p reactionwith the Σ− beam momentum of 0.45< p(GeV/c) <0.55. The red points in Fig. 50 areobtained from the events which satisfy the closest distance cut and include not only thereal Σ−p scattering events but also the unavoidable background. In order to derive thedifferential cross section, we fitted the histograms by the Gauss peak for the signal and 1storder polynomial background as shown in Fig. 50. The differential cross section is obtainedfrom the integral of the Gauss peak. The green points represent the estimated backgroundfrom the large closest distance region as shown in Fig. 51. From the simulation, it is studiedthat the estimated background can not reproduce the background distribution of the redhistogram perfectly. However, this estimated background can be a reference. Here, we alsoderived the differential cross section by subtracting the red histogram and green histogramin the peak region. We check the difference between these two methods, fitting methodand subtraction method. This difference due to the background estimation is shown as thehatched histogram in the differential cross section shown in the next subsection.

43

E (MeV)Δ-30 -20 -10 0 10 20 30

dE

(m

b/s

r/M

eV)

Ω/dσ

2d

0

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0.4

0.6

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1

dE 1}Ω/d{}σd{

< -0.8CMθ-0.9 <= cos

E (MeV)Δ-30 -20 -10 0 10 20 30

dE

(m

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r/M

eV)

Ω/dσ

2d

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dE 2}Ω/d{}σd{

E (MeV)Δ-30 -20 -10 0 10 20 30

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dE 3}Ω/d{}σd{

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E (MeV)Δ-30 -20 -10 0 10 20 30

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eV)

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dE 4}Ω/d{}σd{

< -0.5CMθ-0.6 <= cos

E (MeV)Δ-30 -20 -10 0 10 20 30

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< 0.0CMθ-0.1 <= cos

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eV)

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E (MeV)Δ-30 -20 -10 0 10 20 30

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E (MeV)Δ-30 -20 -10 0 10 20 30

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E (MeV)Δ-30 -20 -10 0 10 20 30

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σ2

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σ2

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< 0.9CMθ0.8 <= cos

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σ2

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E (MeV)Δ-30 -20 -10 0 10 20 30

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eV)

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σ2

d

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dE 20}Ω/d{}σd{

< 1.1CMθ1.0 <= cos

Figure 50: The double differential cross sections d2σ/dΩdE are shown for each scatteringangle. The red points are obtained from the events which satisfy the closest distance cut andinclude not only the real Σ−p scattering events but also the unavoidable background. Thegreen points represent the estimated background from the large closest distance region. Theblack lines (signal+background and only background) show the fit result assuming the Gausspeak and 1st order polynomial background. The differential cross section is the obtainedfrom the integral of the Gauss peak.


Distance (mm)0 5 10 15 20 25 30 35 400

2000

4000

6000

8000

10000

12000

14000


p scattering-Σ

np scattering

p scattering-π

p)-Σratio (<5) = 0.972 (

ratio (<5) = 0.569 (np)

p)-πratio (<5) = 0.570 (

Background selection

Closest Distance (priVtx=p)

Figure 51: Background selection using the large closest distance region. The green plot in50 shows the contribution of events from this region.

44

5.8 Differential cross section of the Σ−p elastic scattering

We derive the Σ−p differential cross section. The data set is generated from 16×106 Σ−

beam and the total cross is assumed to be 30 mb with a flat angular distribution, i.e. 2.4mb/sr. Top two histograms in Fig.52 shows the obtained differential cross sections for thetwo momentum regions. The obtained spectra show the flat distribution for the reasonableacceptance region. The absolute value is still different, and we need further detailed study.However, in the proposed experiment, the differential cross section can be measured withmuch better accuracy. Bottom two histograms in Fig.52 shows the obtained differential crosssections with a half Σ− beam.

In the figures, the two theoretical calculations, the Nijmegen model and the Quark Clustermodel, are also shown. In this reaction, there is no large difference between two theoreticalpredictions. Therefore in this reaction, to test the theoretical framework, we have to provide agood statistics data which constraint the angular dependense of the theoretical predictions.Because the obtained cross section can reproduce the flat distribution assumed in eventgenerator, the expected results can be a constraint for the theoretical models even if thestatistics is half.

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

(m

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/dσd

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p scattering (0.45 < p(GeV/c) < 0.55)-ΣFitting method

Difference of background estimation

500MeV/c NSC97a

500MeV/c NSC97c

500MeV/c NSC97f

550MeV/c fss2

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

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/dσd

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600MeV/c NSC97a

600MeV/c NSC97c

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550MeV/c fss2

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

(m

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/dσd

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500MeV/c NSC97a

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

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/dσd

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600MeV/c NSC97a

600MeV/c NSC97c

600MeV/c NSC97f

550MeV/c fss2

Figure 52: The expected differential cross section of the Σ−p scattering in the beam mo-mentum regions of 0.45 < p (GeV/c) < 0.55 (left) and of 0.55 < p (GeV/c) < 0.65 (left).The differential cross section is the obtained from the integral of the Gauss peak of thed2σ/dΩdE. The hatched histogram shows the difference with the different background sub-traction method where the cross section is obtained as subtraction of the read and greenpoints at the peak region in Fig. 50.

45

5.9 Differential cross section of the Σ−p → Λn inelastic scattering

Fig. 53 shows the obtained differential cross section in the same condition with the Σ−pscattering. The top two histograms show the results with the 16 × 106 tagged Σ− beamand the bottom two histograms show the results with a half beam data. In the Σ−p → Λnreaction, the background contamination is quite small because the energy of the protonfrom the Λ decay has a rather high energy due to the Q value at the decay and kinematicsis separated from other reactions. The data with a wide scattering angle can also be taken.

In the figures, the two theoretical calculations, the Nijmegen model and the Quark Clustermodel, are also shown. The tendency of the angular dependence is similar for the twopredictions although behaviour around cos θ > 0.2 is different. We have wider acceptancefor the scattering angle for this channel. This enable us to test the theoretical model for thiswide scattering angle.

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

(m

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r)Ω

/dσd

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Simulation

500MeV/c NSC97a

500MeV/c NSC97c

500MeV/c NSC97f

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

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Fitting method600MeV/c NSC97a600MeV/c NSC97c600MeV/c NSC97f550MeV/c fss2

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

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Simulation

500MeV/c NSC97a

500MeV/c NSC97c

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

(m

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r)Ω

/dσd

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Fitting method600MeV/c NSC97a600MeV/c NSC97c600MeV/c NSC97f550MeV/c fss2

Figure 53: Differential cross section of the Σ−p → Λn inelastic scattering in the beammomentum regions of 0.45 < p (GeV/c) < 0.55 (left) and of 0.55 < p (GeV/c) < 0.65 (left).

46

5.10 Differential cross section of the Σ+p elastic scattering

The differential cross section of the Σ+p scattering is also derived using the simulated data of55× 106 tagged Σ+ beam. Fig. 54 and Fig. 55 show the obtained spectra for the Σ+ → pπ0

and the Σ+ → nπ+ decay modes, respectively. Because the background contributions forthe two decay modes are different, the cross sections are derived for each channel.

In this channel, the theoretical prediction is very different by the treatment of the hardcore. The Quark Cluster model predicts about twice larger cross section than that of theNijmegen model. The purpose of the Σ+p channel is to test the theoretical models and toconfirm the effect of the quark Pauli effect by providing a good statistics data. The expectedspectrum fulfills the purpose and enable us to confirm the difference due to the hard core.

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

(m

b/s

r)Ω

/dσd

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0.5

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5Fitting method


450MeV/c NSC97a

450MeV/c NSC97c

450MeV/c NSC97f

450 MeV/c FSS

450 MeV/c fss2

mode)0πp→+Σp scattering (0.4 < p(GeV/c) < 0.5) (+Σ

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

(m

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r)Ω

/dσd

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5 Fitting method


450MeV/c NSC97a

450MeV/c NSC97c

450MeV/c NSC97f

550 MeV/c FSS

550 MeV/c fss2

mode)0πp→+Σp scattering (0.5 < p(GeV/c) < 0.6) (+Σ

Figure 54: Differential cross section of the Σ+p elastic scattering in the beam momentumregions of 0.4 < p (GeV/c) < 0.5 (left) and of 0.5 < p (GeV/c) < 0.6 (left) for the Σ+ → pπ0

decay mode.

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

(m

b/s

r)Ω

/dσd

0

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450MeV/c NSC97a

450MeV/c NSC97c

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450 MeV/c fss2

mode)+πn→+Σp scattering (0.4 < p(GeV/c) < 0.5) (+Σ

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

(m

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r)Ω

/dσd

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Fitting method


450MeV/c NSC97a

450MeV/c NSC97c

450MeV/c NSC97f

550 MeV/c FSS

550 MeV/c fss2

mode)+πn→+Σp scattering (0.5 < p(GeV/c) < 0.6) (+Σ

Figure 55: Differential cross section of the Σ+p elastic scattering in the beam momentumregions of 0.4 < p (GeV/c) < 0.5 (left) and of 0.5 < p (GeV/c) < 0.6 (left) for the Σ+ → nπ+

decay mode.

47

6 Time schedule, cost and man power

We are going to use the present detector systems in the K1.8 beam line as many as possible.Additionaly, we will construct detectors dedicated for the proposed experiment such as thefiber trackers and the detector system surrounding the LH2 target. Fig. 56 shows theschedule of the preparation of the newly developed detectors for the proposed experiment.In Table 7, we summarized new items for the proposed experiment.

Scince 2009, we started the R&D for the multichannel readout circuit for PPD(MPPC)with a support from KEK and LAL. The SPIROC-A chip is the most multi-purpose ASICand we are developing the readout board with SPIROC-A for the fiber trackers. The boardhas the SiTCP readout which enables us to merge it with the present DAQ system. Theexisting TDC system for the wire chambers can be used for the fiber tracker readout byconntecting the digital output from SPIROC board. We can exchange the beam line fibertracker from the wire chambers.

For the LH2 target, we will make a low material target vessel and vacuum window systemso as to detect a low energy proton with a support of a LH2 target group in KEK.

FY2010 FY2011 FY2012 FY2013

R&D of SPIROC boardProduction of fiber trackerfor vertex detector

Production of fiber trackerfor beam line tracker

CDC design and prduction

Calorimeter production

Design of LH2 target Test with surroundig detector

FY2014

Σ-p scattering beam time

Analysis and debug

Σ+p scattering beam time

Figure 56: Schedule of the preparation for the proposed experiment

References

[1] M. M. Nagels et al., Phys. Rev. D15 (1977) 2547; D20 (1979) 1633; P. M. Maessen et al.,Phys. Rev. C40 (1989) 2226; Th. A. Rijken et al., Nucl. Phys. A547 (1992) 245c.

[2] M. Oka and K. Yasaki, Quarks and Nuclei, et. W. Weise, Vol 1 (World Scientific, 1984)489; K. Yazaki, Nucl. Phys. A479 (1988) 217c; K. Shimizu, Nucl. Phys. A547 (1992)265c.

[3] Y. Fujiwara, C. Nakamoto, Y. Suzuki, Prog. Theor. Phys. 94 (1995) 214; 94 (1995) 353;Phys. Rev. Lett. 76 (1996) 2242; Phys. Rev. C54 (1996) 2180.

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Item Cost [kJY]Beam AnalyzerFiber tracker New 1,000

Readout MPPC New 3,600SPIROC board New 8,000Multihit TDC Existing 0

LH2 target New 5,000Detector for scattered proton

Fiber tracker New 1,000Readout MPPC New 4,500SPIROC board New 15,000

Cylindrical chamber New 10,000Readout Amp & Discri Reuse of MWPC and MPDC 0

Calorimeter Reuse of Neutron counter 0

Table 7: A list of items newly needed for this experiment.

[4] Y. Fujiwara, Y. Suzuki, C. Nakamoto, Prog. Nucl. Part. Phys. 58 (2007) 439.

[5] T. Inoue et al., HAL QCD collaboration, arXiv:1007:3559 [hep-lat]

[6] R. Engelmann et al. Phys. Lett. 21 (1966) 587; B. Sechi-Zorn et al. Phys. Rev. 175 (1968)1735; G. Alexander et al. Phys. Rev. 173 (1968) 1452; J. A. Kadyk et al. Nucl. Phys. B27 (1971) 13; F. Eisele et al. Phys. Lett. B 37 (1971) 204.

[7] O. Hashimoto and H. Tamura Prog. Nucl. Part. Phys. 57 (2006) 564.

[8] Y. Kondo et al. Nucl. Phys. A 676 (2000) 371

[9] J.K. Ahn et al. Nucl. Phys. A 761 (2005) 41.

[10] T. Kadowaki et al. Eur. Phys. J. A 15 (2002) 295.

[11] J. Asai et al. Jpn. J. Appl. Phys. 43 (2004) 1586.

[12] T. Nagae et al. Phys. Rev. Lett. 80 (1995) 1605.

[13] H. Noumi et al., Phys. Rev. Lett. 89 (2002) 072301, P.K. Saho et al. Phys. Rev. C 70(2004) 044613.

[14] M. Kohno et al. Phys. Rev. C 74 (2006) 064613.

[15] T. Harada and Y. Hirabayashi, Nucl. Phys. A767 (2006) 206.

[16] R. Jastrow, Phys. Rev. 81 (1950) 636.

[17] M.L. Good and R.R. Kofler, Phys. Rev. 183 (1969) 1142.

[18] D.J. Candlin et al. Nucl. Phys. B226 (1983) 1.

[19] B. Conforto et al. Nucl. Phys. B105 (1976) 189.

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[20] http://omega.in2p3.fr/

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Measurement of the cross sections of Σp scatterings

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Transcript of Measurement of the cross sections of Σp scatterings