Scattering Observables of the N Nand Y N Interactions in the SU 6 Quark Model

Transcription

1 931 Prgress f Theretical Physics, Vl. 1, N.5, Nvember 1998 Scattering Observables f the N Nand Y N Interactins in the SU 6 Quark Mdel Tadashi FUJITA, Yshikazu FUJIWARA, Chki NAKAMOTO* and Yasuyuki SUZUKI** Department f Physics, Kyt University, Kyt , Japan *Suzuka Natinal Cllege f Technlgy, Suzuka , Japan ** Department f Physics, Niigata University, Niigata , Japan (Received July 6, 1998) Scattering bservables f the N N and Y N interactins are investigated in a recent quark mdel develped fr the simultaneus deseriptin f the N Nand Y N systems. The mdel is frmulated in the (3q)-(3q) resnating-grup methd and incrprates a phenmenlgical quark-cnfining ptential, the full Fermi-Breit interactin with explicit quark-mass dependence, and minimum effective mesn-exchange ptentials f scalar and pseud-scalar mesn nnets directly cupled t quarks. The differential crss sectins and sme spin bservables f the np and pp scattering are reasnably reprduced. Predictins fr the E+p and Ap scattering bservables at intermediate energies are very much mdel-dependent, suggesting the imprtance f further experimental studies n these quantities. 1. Intrductin The nuclen-nuclen (N N) and hypern-nuclen (Y N) interactins are amngst the mst imprtant fundamental interactins which result frm highly nn-trivial quark-glun dynamics gverned by quantum chrm dynamics (QCD). Since QeD is nt amenable t the direct slutin f lw-energy hadrn phenmena, QCD-inspired effective quark mdels are usually emplyed t study these interactins. The cmpsite nature f the nuclen and hypern is taken int accunt mst straightfrwardly in the resnating-grup methd (RGM). In the simplest RGM frmulatin fr the N N interactin, 1) the effective quark-quark (qq) interactin is usually built by cmbining a phenmenlgical quark-cnfining ptential with a ne-glun exchange ptential thrugh the clr analg f the Fermi-Breit (FB) interactin. This simple (3q)-(3q) mdel culd elucidate nly the extreme shrt-range part f the N N interactin, which was fund t be purely repulsive. Since the lng-range part f the interactin is dminated by mesn-exchange effects, any RGM descriptin in the simple (3q) (3q) mdel must cmprise effective mesn-exchange ptentials (EMEP) intrduced by sme apprpriate means. Meanwhile, many successful mesn-exchange descriptins f the N N interactin have been extended t the Y N interactin. These include several versins f the nebsn exchange ptentials (OBEP), such as the Nijmegen mdels 2)-4) and the Jiilich ptentials. 5),6) In these mdels a large number f baryn-mesn cupling cnstants are cnstrained by the use f the SU3 relatins, and several SU3 parameters are determined t reprduce the N N prperties tgether with the lw-energy crsssectin data fr the Y N scattering. One can inherit many techniques develped Dwnladed frm n 24 Nvember 217

2 932 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki here fr incrprating EMEP in the quark mdel. The extensin f the (3q)-(3q) RG M study f the N N interactin t the Y N interactin is, hwever, by n means straightfrward, since the lack f the medium-range attractin in the quark mdel leads t excessive ambiguity in the way f supplementing EMEP. Furthermre, in the study f the Y N interactin, the flavr-symmetry breaking shuld be crrectly intrduced even thugh we chse the spin-flavr SU 6 symmetry as a starting pint. We have recently btained a simultaneus descriptin f the N Nand Y N interactins in the RGM frmulatin f the spin-flavr SU6 quark mdel. 7),8) This frmulatin incrprates EMEP induced frm the scalar (S) and pseudscalar (PS) mesn nnet exchanges at the quark level, and calculates the spin-flavr factrs fthe quark-exchange kernel explicitly by assuming the Gell-Mann matrices fr the flavr peratrs f the ctet-mesn exchange ptentials. Since the hypern and nuclen belng t the same class f the spin-flavr SU6 supermultiplet 56, the spin-flavr factrs thus evaluated give a strng cnstraint n the parameters f the EMEP. The micrscpic apprach t intrduce EMEP at the quark level gives a strng crrelatin amng different flavr channels f the N Nand Y N interactins, making it pssible t utilize the very rich experimental infrmatin f the N N interactin fr the study f the Y N interactin with sca.rce experimental infrmatin. In Refs. 7) and 8) we have fixed mdel parameters by using sme apprpriate N N prperties and the available lw-energy "ttal" crss sectin data fr the Y N scattering, and fund that the deutern prperties and the N N phase shifts up t the partial waves J S 4, as well as the lw-energy Y N differential crss sectins, are reprduced reasnably well. In Ref. 9) we have shwn that, fr sme particular energies, reasnable agreement with the experimental data is btained nt nly fr the ttal and differential crss sectins but als fr sme spin bservables f the np and pp systems. A similar analysis is als carried ut in Ref. 1) fr E+p scattering at PE = 45 MeV Ie, in which a strng crrelatin between the resnance behavir f varius OBEP mdels and the predicted differential crss sectins and plarizatin is discussed. In this investigatin, we cntinue ur study f the scattering bservables f the N Nand Y N systems. The reasn we need t examine the scattering bservables in additin t the phase shifts is as fllws: 1) In the Y N system, phase-shift analysis des nt seem t be pssible even in the future, because f the very pr statistics f the experimental data. 2) In the N N system where the phase-shift analysis exists, we can determine the quality f ur mdel predictins fr reprducing the experimental data. This infrmatin is indispensable when we attempt t analyze future Y N data by using ur quark mdel. 3) Since ur quark mdel is nt perfect in reprducing the N N phase shifts, it is useful t pinpint the flaw f the predicted scattering bservables fr the future renvatin f ur quark mdel. It is certainly true that each cmpnent f the interactin is usually reflected mre clearly in the behavir f the phase shifts as lng as the energy is nt high. In the studies f the Y N interactin using the OBEP mdels, hwever, the cmbined discussin f the phase-shift behavir and the scattering bservables is nt frequently undertaken, since the parameters f OBEP's are suppsed t embdy the charac- Dwnladed frm n 24 Nvember 217

3 Scattering Observables f the N Nand Y N Interactins 933 teristics f the experimental data. In the present framewrk, the shrt-range part f the N Nand Y N interactins is unambiguusly determined. It wuld be useful t examine the crrelatin between the phase-shift behavir and that f the scattering bservables by taking advantage f the strng crrelatin f the N Nand Y N interactins in ur quark mdel. We stress that ur purpse in studying the N Nand Y N interactins in the quark mdel is nt t reprduce the experimental data t the utmst accuracy, but t clarify the varius aspects f the baryn-baryn interactins such as the rle f nn-central frces and the rich spin-flavr cntent. The dynamical prcesses taking place between the cmpsite systems f quarks are dminated by the effective qq interactin as well as imprtant kinematical requirements arising frm the quark Pauli principle and the symmetries f the spin, flavr and clr degrees f freedm. In particular, it is a great advantage f the RGM framewrk that we can deal with the N Nand Y N interactins n an equal fting as lng as we assume the SU6 wave functins fr the baryns and use a unique qq interactin between quarks. In ur quark mdel study, the perfect reprductin f the experimental data f the N N system is nt a mandatry cnditin t prceed t the study f the scattering bservables f the Y N system, but mre imprtant is that the varius pieces f the interactin are well balanced. We expect that this is reflected in the energy dependence and shapes f the angular distributins f varius scattering bservables. The present discrepancies between the predicted and empirical N N phase shifts and the scattering bservables cannt be easily vercme by a mere change f the parameter values. Further imprvement requires majr renvatin f the present quark mdel r the present framewrk. This viewpint is largely different frm thse f previus quark-mdel studies f the N N scattering bservables. Fr example, the Paris grup 11) cmbined the quark-mdel ptential 12) with the lng- and medium-range part f the Paris ptential, by intrducing a special type f cutff functin. They tested the quality f the mdel by cnfrnting its predictins directly with data n scattering bservables, and fund that the fit t the existing pp data was nt satisfactry. It is nt apprpriate, hwever, t substitute the quark-mdel ptential fr the shrt-range part f the Paris ptential. One shuld allw the quark mdel the freedm t chse an ptimum framewrk fr the EMEP. Anther calculatin f the spin bservables by the Tiibingen-Salamanca grup 13),14) is mtivated by the hpe that ne culd find additinal infrmatin n the quark degrees f freedm at shrt distances. They als attempt t estimate the quality f the quark-mdel predictins fr the plarizatin bservables in the N N system. The extensin t the Y N system is their future wrk. In this paper, we first extend ur wrk in Ref. 9) and examine the energy dependence f the NN scattering bservables up t abut 3 MeV. This is a necessary step t make sure that ur quark mdel includes majr ingredients fr the qualitative descriptin f the N Nand Y N interactins up t certain incident energies. Since a detailed discussin f the E+p scattering bservables at intermediate energies is already made in Ref. 1), we briefly mentin characteristics f the varius mdels, which appear in the energy dependence f the differential crss sectins and Dwnladed frm n 24 Nvember 217

4 934 T. Fujita, Y. Fujiwam, C. Nakamt and Y. Suzuki plarizatin. Next we prceed t analyze the Ap system, fr which new experimental data are expected frm KEK in the near future. 15) In this system the cupling with the EN(! = 1/2) channel thrugh the antisymmetric LS frce (LS(-) frce) is particularly imprtant at the cusp regin, althugh we remain in this paper in the energy regin where the EN channel is still clsed. The result f ur preceding mdel, RGM-F, 16) - 18) is mentined nly briefly when sme discrepancy with FSS and RGM-H appears. In the next sectin we frmulate the mdel t calculate the N Nand Y N scattering bservables. After a brief discussin f ur quark mdel, the prcedure t calculate the scattering bservables frm the S-matrix is utlined. Sectin 3 deals with results and cntains discussin. The differential crss sectins and the spin bservables f the np and pp scattering are examined in 3.1, thse f the E+ p scattering in 3.2 and thse f the Ap scattering in 3.3. The final sectin is devted t summary Quark mdel 2. Frmulatin Here we nly recapitulate sme imprtant features f ur quark mdel. Our new versins, FSS 7), 8) and RGM-H,8) and the previus versin RGM-F 16) -18) are frmulated in the (3q)-(3q) RGM applied t the system f tw (8)3 clusters, where the quark interactin is cmpsed f the full FB interactin with explicit quark-mass dependence, a simple cnfinement ptential f a quadratic pwer law and EMEP acting between quarks. The RGM equatin derived frm the variatinal principle (8lJi1E - HllJi) = is frmulated fr the parity-prjected relative wave functin X7r (R) as 8) [ C + 21i2 (a~)2-2: Vd~N)~(R) - 2: Vd~)~(R) - 2: vd1n)~(r) (SI2) 1 ~ ~ ~ ~ xx~(r) = 2:! dr' [ 2:M~~~(R, R') - CO M~O/(R, R')] X~/(R'), (2 1) ' fl where C is the relative energy in the channel :. Each channel is specified by a set f quantum numbers : = [1/2(1l)a}, 1/2(1l)a2l SSzY liz; P, where P is the flavrexchange symmetry phase. 16) The summatin ver n fr the exchange kernel M~~~ invlves nt nly the exchange kinetic-energy (K) term, but als varius pieces f the FB interactin, as well as several cmpnents f EMEP. The FB interactin invlves the clr-culmbic (CC) piece, the mmentum-dependent Breit retardatin (MC) piece, the clr-magnetic (GC) piece, the symmetric LS (sl8) piece, the antisymmetric LS (al8) piece, and the tensr (T) piece. The EMEP cntributin, n the ther hand, yields the central (CN) cmpnent frm the S-mesns and the spin-spin (S8) and tensr (TN) terms riginating frm PS mesns. These terms are further divided int cntributins frm sme particular mesn species dented by {3, which Dwnladed frm n 24 Nvember 217

5 Scattering Observables f the N Nand Y N Interactins 935 Table I. Quark-mdel parameters, SU 3 parameters f the EMEP, S-mesn masses, and the reductin factr C6 fr FSS and RGM-H. The parameters as and a Ps dente the F/(F + D) ratis fr the flavr-ctet SU 3 cupling cnstants. The IO-mesn mass dented by "tw-ple" indicates a tw-ple apprximatin, fr which mlc 2 (13I) and m2c 2 (132) are shwn belw the table. b (fm) m"dc2 (MeV) as,\ = m./m"d FSS RGM-H n f~ (Js (deg) as FSS & 1 RGM-H b Jrs ffs (JPs (deg) a Ps FSS /5 RGM-H /5 m,c 2 (MeV) ms*c 2 (MeV) m6c2 (MeV) m~c2 (MeV) FSS RGM-H tw-ple c C6 FSS.381 RGM-H.339 a OS = 65 is used in the EN(I = 3/2) channel. b as = 1 fr nn-isscalar mesns. c MeV (.169) and MeV (.6132).2) is explicitly shwn in Eq. (2 1) nly fr the direct ptentials. The difference f the three versins, RGM-F, FSS and RGM-H, lies slely in the mesn species, the interactin types, and the treatment f the spin-flavr factrs fr the EMEP assumed t act between quarks. In RGM-F nly the ne-pin exchange and K-mesn exchange tensr frces are taken int accunt, in additin t the S mesn nnet (t, S*, 8 and ~) exchanges, while in FSS and RGM-H all pieces f the PS-mesn nnet (r7', "1, 71' and K) are intrduced with respect t the spin-spin and tensr terms. Cupling cnstants f these mesns t quarks are cntrlled by the SU3 cupling cnstants appearing in the direct term f the RGM equatin, and are determined t realize an ptimum fit t sme f the N N prperties and available lw-energy "ttal" crss sectins fr the Y N scattering. The N N prperties fitted are the deutern binding energy, ISO scattering length fr np (FSS) r pp (RGM-H) scattering, and S- and P-wave phase shifts up t abut 2 MeV, adjusted t the recent phase-shift analysis by the Nijmegen grup. 19) Since Table III f Ref. 8) has a misprint fr frs and fr s f RGM-H, we give the crrect mdel parameters f FSS and RGM-H in Table 1. The spin-flavr factrs f the EMEP are nt explicitly calculated in RGM-F. In this mdel the exchanged mesns are first assumed t be flavr-singlet, and then the verall strength is adjusted such that the flavr dependence f the spin-flavr factrs in the direct term crrectly reprduces the flavr dependence f the Nijmegen mdel F, which is determined frm the prducts f the baryn-mesn cupling cnstants with the SU3 relatins. Fr scalar mesns the strengths f the riginal mdel-f parameters are multiplied by a cmmn reductin factr, C+l =.56 fr the flavr symmetric states with P = +1 and C--l =.4212 fr the flavr antisymmetric states Dwnladed frm n 24 Nvember 217

6 936 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki with P = -1. These are determined t reprduce the 1 S phase shift f the N N scattering and the crrect binding energy f the deutern. On the ther hand, the spin-flavr factrs f EMEP are explicitly calculated in FSS and RGM-H. We have fund that the full micrscpic apprach in these mdels impses t strict a cnstraint n the SU3 EMEP parameters. Fr example, the F/(D + F) rati f the flavr ctet mesns is n lnger a free parameter, but takes specific SU6 values riginating frm the SU6 spin-flavr wave functins f the ctet baryns. The pure electric nature f the S-mesns with as = 1 leads t the difficulty that the direct ptentials fr the AN and EN systems becme identical. Under this cnstraint it is nt easy t ensure an apprpriate relative strength f the central attractin between AN and EN channels. In particular, the central attractin f the E+p channel is usually t strng if we fix that f the AN channel t fit the lw-energy Ap crss sectins. In FSS we avid this difficulty by chsing a slightly larger value f OS fr the isscalar mesn mixing nly fr the EN(J = 3/2) system. In RGM-H we partially return t the ld prescriptin f RGM-F and revise a degree f freedm f as by using the apprximate spin-flavr-clr factrs nly fr the isscalar S-mesns t and S*. A shrt cmment fllws regarding the spin-spin part f the PS mesn exchange ptentials and their cupling cnstants. The spin-spin part includes a delta-functin type cntact term which has recently been advcated by sme authrs 21) as a replacement f the clr-magnetic term f the FB interactin. In fact this term als yields the shrt-range repulsin in the S-wave channels f the N N interactin. Hwever, we are reluctant t take this cntact term f EMEP as the rigin f the very intricate flavr dependence f the baryn-baryn interactin. We have intrduced a cmmn reductin factr C fr this term and determined the value in the N N system. In ur previus frmulatin,8) we included the factr (m(3/m 7r +)2 cmmn t the spin-spin and tensr terms f the PS mesn exchange ptentials. In the actual calculatin f FSS and RGM-H, hwever, this mass factr is intrdticed nly fr the spin-spin term Scattering bservables We slve the cupled-channel RGM equatin Eq. (2 1) by the variatinal methd, emplying Gaussian-type trial functins. 22) The S-matrix thus btained cnstitutes the basic building blcks fr the scattering amplitude which is expressed by eight invariant amplitudes a,..., h: 23) 1 M = "2 {(a + b) + (a - b)(o"l. n)("2 n) + (c + d) ("1 m)("2 m) +(c - d)(o"l l)("2 l) + e ("1 + "2). n + f ("1 - "2). n +g {("1 l)("2. m) + ("1. m)("2 l)} +h {("1 l)("2. m) - ("1. m)("2 l)}}, (2 2) where Dwnladed frm n 24 Nvember 217

7 Scattering Observables f the N Nand Y N Intemctins 937 l = kf + k i Ikf + kil ' (2 3) and k i and k f are unit vectrs f the incident and scattered particles in the centerf-mass (c.m.) system. The partial-wave expansin f the invariant amplitudes are given in Eq. (3) f Ref. 24) fr a,, e, and in Eq. (2.21) f Ref. 23) fr f, g, h. The last three amplitudes, J, 9 and h, d nt appear fr the N N scattering, since the prcess is invariant under the exchange f tw particles (f and h) and time reversal (g and h). The time reversal prperty als excludes 9 and h even in the elastic Y N scattering. These three terms crrespnd t the nn-central frces characteristic f Y N scattering; i.e, J crrespnds t 8(-), 9 t (r, p), and h t 8(-)<7 (i.e., the (L S(-))P<7 term), respectively. 25) In particular, 8(-) and 8(-)<7 interactins invlve the spin change between and 1, tgether with the transitin f the flavr-exchange symmetry P f- P'. In N N scattering this is frbidden by isspin cnservatin, since the flavr-exchange symmetry is uniquely specified by the isspin: P = (_1)1-1. On the ther hand, these interactins are all pssible when the AN-EN transitin is incrprated int the Y N scattering, leading t intriguing interplay f nn-central frces. The standard prcedure t derive the plarizatin bservables f the N Nand Y N scattering is frmulated in terms f the spin density matrix given by (2 4) where fl, l/ =, l, m and n dente the cmpnents f the spin vectrs f the first and secnd particles with respect t the unit vectrs l, m and n in Eq. (2 3). When the plarizatin f the particle i = 1 r 2 is nt measured, we assume fl, l/ = and (JiO = 1. The density matrix f the spin variables in the utging channel is related t that in the incident channel thrugh pscat = M PincMt. The differential crss sectin is given by (2 5) where "() = (1/4) Tr[MMt] is the differential crss sectin when the incident and target particles are bth unplarized. In Eq. (2 5) the plarizatin matrix X",).p,v is defined by (2 6) Any plarizatin bservables in the c.m. system can be calculated frm the plarizatin matrix Eq. (2 6) thrugh (2 7) Dwnladed frm n 24 Nvember 217

8 938 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki Frm the definitin Eq. (2 6), it is clear that all tgether 44 = 256 matrix elements f X",>.J.lV are expressed as linear cmbinatins f 64 real prducts, JaJ2, JbJ2,..., Re[a*b], SSm[a*b],... An elegant prcedure t derive all the explicit expressins f the 64 independent bservables as linear cmbinatins f these is given by Bystricky, Lehar and Winternitz 26) in their frmulatin f the thery f scattering bservables fr the N N system. The final result fr the mst general scattering amplitude Eq. (2 2) invlving spin-1/2 particles is tabulated in Table I f Ref. 23). The transfrmatin f the spin bservables expressed in the unit vectrs land m in the c.m. system t thse expressed in the bdy-fixed frame in the labratry system invlves nt nly a trivial kinematical rtatin arund the n axis, but als an extra rtatin arund the same axis, which was referred t by Stapp 27) as the relativistic rtatinal crrectin f the plarizatin vectrs. The angles,!h and DR, by which the plarizatin vectrs f the scattered and recil particles are rtated, respectively, are btained as a result f three successive Lrentz transfrmatins with nn-parallel velcity vectrs. 6), 27), 28) The spin bservables in the labratry system, incrprating these relativistic crrectins, are als given in Table II f Ref. 23) in the mst cmpact frm. The relatinship between a, (3 in Eq. (3.8) f Ref. 23) and DL, DR in Eq. (B.7) f Ref. 6) is given by. () a = fh - 2" + ()L, (2 8) where ()L (()R) is the scattering (recil) angle in the labratry system and () is that in the c.m. system. Fr elastic scattering, the simple relatins DL = () - 2()L = 2a and DR = -71" + () + 2()R = -71" + 2(3 hld. 6) 3.1. N N scattering 3. Results and discussin In this subsectin we discuss scattering bservables f the N N system predicted in the present quark mdel. Since the mdel parameters are fixed by fitting the S wave and P-wave phase shifts up t the energy range 71ab :::; 2 MeV, the lw-energy scattering bservables are naturally reprduced quite well. Hwever, the phase shifts f higher partial waves are nly qualitatively reprduced. Fr example, in FSS and RGM-H (and als in RGM-F) the 3 D2 phase shift is t attractive by mre than 1 in the energy range 2 MeV - 3 MeV,8) which seems t be a cmmn feature f mst quark-mdel calculatins (see, fr example, Ref. 12)). The deviatin f the E2 mixing parameters f the 3 P 2-3 F2 cupling is als nt small. These features indicate sme insufficiency f the present mdel in the tensr and/r quadratic LS cmpnents, which may be related t ur assumptin implicit in the exclusin f vectr mesns. The differential crss sectins (da/dd) and the plarizatin (P) fr the np scattering, predicted by ur quark mdel, are displayed in Fig. 1, and thse fr the pp scattering in Fig. 2. The slid curves indicate results by RGM-H, and the dashed curves thse by FSS. Partial waves up t the ttal angular mmentum Jrnax = 7 are taken int accunt. Cmparisn with the experimental data 29) shws that quali- Dwnladed frm n 24 Nvember 217

9 Scattering Observables f the N Nand Y N Interactins RGM-H - FSS --- T 1ab = 5 MeV ~--~---+--~~--+---~ ~ ~--~--~ Tlab = 97 MeV i T1ab = 1 MeV -.4 a 1--~--+-~--+---~--I ~--4--~--~--l D.. 15 T 1ab = 212 MeV.6 'C'5 -.2 " Tlab = 22 MeV -.4 I--+---~-~ r---I r ~--~--~ Tlab = 32 MeV L-_~ -L ~ ~ -L ~ ~ -L ~ L- ~ ~ a c.rn. (deg) a c.rn. (deg) Fig. 1. Cmparisn f the quark-mdel np differential crss sectins and plarizatin with experimental data. The slid curve dentes the result by RGM-H, and the dashed curve that by FSS. The mdel calculatin takes int accunt the partial waves up t Jrnax = 7. The experimental data are taken frm Ref. 29). -.4 tative agreement is achieved in these cases. In np scattering, the differential crss sectin data shw a typical V-shape behavir. The peak psitin fr the plarizatin data is enhanced and mves gradually t the frward angles as the incident energy increases. Our quark mdel reprduces these features quite well. There are, hwever, sme deviatins frm the experimental data at higher energies. In the differential crss sectins, ur quark mdel gives t large values at Oem ~ 3 and Dwnladed frm n 24 Nvember 217

10 94 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki 15 r-~----' ~ ' ' r , T 1ab = 5 MeV RGM-H FSS T 1ab = 52 MeV ;:- :a 5 '" " ill,.... T 1ab = 95 MeV E a I-r------f i ~ ~::..:.:-::~-~;~~~-~:~:~-;.=-.;-~~~--~-~:~~~-~.~~ ~-=~J T 1ab = 144 MeV T 1ab = 142 MeV 1--r f :\._ T 1ab = 212 MeV T 1ab = 213 MeV ' :' ' ' ' ' ' -.2 W W 6 8 c.m. (deg) 8 c.m. (deg) Fig. 2. The same as Fig. 1 but fr pp differential crss sectins and plarizatin..2 yields a bump structure arund Oem =: 13. Sme deviatins frm the experimental data, especially at Oem = 3-6 and Oem = 9-15, are als seen in the plarizatin at 31 MeV. Fr the pp scattering in Fig. 2, the differential crss sectins and the plarizatin are pltted nly fr Oem :-s: 9, since these are repeated fr Oem = Althugh ur mdel (especially FSS) verestimates the differential (and cnsequently "ttal") crss sectins, the energy dependence and the shape f the angular distributin are reasnably described. The mdel RGM-H gives a slightly better fit t the experimental differential crss sectins, since the parameters f this mdel are fixed by using the pp phase shifts with I = 1. The measured Dwnladed frm n 24 Nvember 217

11 Scattering Observables f the N Nand Y N Interactins 941 plarizatin becmes larger as the en- 1.2,-_,--_--,---,-,-_---,, ergy increases. Our quark mdel reprduces this energy dependence fr the.8 magnitude f the plarizatin. The plarizatin n the high-energy side.4 (Tiab rv 213 MeV) is underestimated t sme extent. The quality f the agreement with T 1ab = 212 MeV experimental results is similar even fr the ther spin bservables. Figures 3.8 (np) and 4,5 (pp) shw the cmparisn f the deplarizatin D and the Wlfenstein parameters, R, R' and A. These ::.4 spin bservables d nt have a simple symmetry prperty with respect t the scattering angles, even fr the pp system Next, we briefly discuss the imprvement f the scattering bservables.4 in RGM-H and FSS ver thse in their preceding versin RGM-F. In the plarizatin and the deplarizatin at 5 «Me V, we d nt find any large deviatin amng these calculatins. On -.4 T the ther hand, the differential crss 1ab = 135 MeV -.8 sectins and the spin crrelatin parameters f RGM-F deviate frm the c.m. (deg) experimental data at backward angles, Fig. 3. Deplarizatin D and Wlfenstein parameters R and A by RGM-H (slid curve) whereas thse f RGM-H and FSS give better results. (See Fig. 1(b) f Ref. H) and FSS (dashed curve) fr the np system, fr the differential crss sectins at 9 cmpared with experimental data. 29) MeV.) We attribute this difference t the lack f the spin-spin term f the PS mesns (especially the pin) in the RGM F. It is interesting t nte that this deviatin appears nly in the differential crss sectins and the spin crrelatin parameters, and nt in the plarizatin and the deplarizatin. This may indicate that sme bservables are very sensitive t the particular cmpnents f the interactin. In the E+p system we will see anther example f this kind f prperty with respect t the resnance behavir f particular partial waves. Summarizing this subsectin, we have fund that the present quark mdel can qualitatively reprduce very rich experimental data f the N N scattering bservables ver a wide energy range up t Tiab ::; 3 MeV. Althugh the quality f the fit is far belw that f the OBEP apprach, the shrt-range prperty and the main part f the spin dependence in the N N interactin are prperly incrprated in ur quark mdel within this energy regin. This is a necessary cnditin fr the purpse f extending Dwnladed frm n 24 Nvember 217

12 942 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki 1. rr---,----,---,---,--, ,----r----,--..., 1..8 T 1ab = 143 MeV T 1ab = 141 MeV h j--+_ h~ t---t-----j---l.8 Tlab = 211 MeV T 1ab = 211 MeV I.6.4 Cl r+.r ~~-~-++_-- ~----~~--_.n a: 1..8 T 1ab = 241 MeV L--~3L--~6~-~9~~1~2~~1~5~-~-~3~-~6~--9~-~12~--1~5~-~18 Sc.m. (deg) Sc.m. (deg) Fig. 4. The same as Fig. 3 but fr pp deplarizatin and Wlfenstein parameters R at varius energies. the present mdel t the Y N interactin. Sme deviatins frm the experimental data fund n the high-energy side shuld be investigated fr the imprvement f the present framewrk E+p scattering The SU3 cntent f the E+p system is (22) fr the flavr-symmetric 1 E and 3 states and (3) fr the flavr-antisymmetric 3 E and 1 states. 16) Since the pp system als has SU3 symmetry (22), the E+p interactin in the 1 E and 3 states is expected t resemble the well-knwn pp interactin as lng as the qq interactin is apprximately SU3 scalar. On the ther hand, the E+p interactin in the 3 E and 1 states is a priri unknwn frm this kind f simple symmetry discussin. In the quark mdel, the mst cmpact (8)6 cnfiguratin f the EN(I = 3/2) 3S 1 state Dwnladed frm n 24 Nvember 217

13 Scattering Observables f the N Nand Y N Intemctins T 1ab = 213 MeV.6.4 ii:: T 1ab = 241 MeV T 1ab = 141 MeV « T 1ab = 213 MeV -.8 T 1ab = 241 MeV Sc.rn. (deg) Sc.rn. (deg) Fig. 5. The same as Fig. 4 but fr pp Wlfenstein parameters R' and A is almst frbidden by the effect f the Pauli principle. The E+p interactin in the 381 state is cnsequently repulsive due t this kinematical effect arising frm the quark structure f the baryns. On the ther hand, the Pauli effect gives a weak attractin fr the 1 PI state thrugh the kinetic-energy exchange kernel in the RG M frmalism. 16) In the OBEP mdel, the phase-shift behavir f the 3 SI and 1 PI states fr PI: ~ 3 MeV Ic is very much mdel-dependent, which results in different predictins f the differential crss sectins and plarizatin at intermediate energies. 1) Fr example, the 1 PI phase shift f the Nijmegen hard-cre mdel-f (HC-F) 3) and mdel-d (He-D) 2) exhibits strng resnant behavir arund 4 MeV Ic, which yields strng enhancement f the differential crss sectins at the frward and backward angles. The Nijmegen sft-cre mdel (NSC),4) n the ther hand, displays Dwnladed frm n 24 Nvember 217

14 944 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki 2.8 PI: = 2 MeV/c 15 RGM-H PI: = 2 MeV/c.6 FSS NSC.4 1 '", HC-F 'x """ '...x.2 't< 5 -:-f~ ~ I ~ ~ :.8 x 15 x 1 PI: = 4 MeV/c -;:-5 x --- PI: = 4 MeV/c x )( x.2 x.!!!. " X,, a. E O PI: = 6 MeV/c ~ " PI: = 6 MeV/c.8 a. ' 15.6 )( x.4 )( 1 " 5 15 PI: = 8 MeV/c )( )( II )(.6.4 )( x.2... "'...r.,.,~ PI: = BOO MeV/c 1 /... )('\ )( I x... I )(.2 )( x I x x x I 5 x a c.rn. (deg) a c.rn. (deg) Fig. 6. Quark-mdel predictins fr E+p differential crss sectins and plarizatin in RGM-H (slid curve) and FSS (dashed curve), cmpared with thse by the Nijmegen sft-cre mdel, NSC (circles), and the hard-cre mdel-f, HC-F (crsses). The results by NSC and HC-F are btained by using the phase-shift values given in Refs. 4) and 3) with the maximum angularmmentum values up t L ~ 2 and L ~ 4, respectively. Fr FSS and RGM-H, partial waves up t Jrna.x = 7 are included a brad resnance structure arund HOO MeV Ie in the 381 phase shift, althugh it is repulsive belw P E ~ 4 MeV I c. The small phase-shift values in the 38 1 state arund this energy result in small values f the differential crss sectins and the plarizatin. The Jiilich mdels 5), 6) als have a brad 38 1 resnance, resulting in Dwnladed frm n 24 Nvember 217

15 Scattering Observables f the N Nand Y N Interactins 945 very small differential crss sectins at 45 MeV/e. 1) These features f the scattering bservables can be clearly seen in Fig. 6, which displays the energy dependence f the 17+ P differential crss sectins and plarizatin up t PE = 8 MeV/e. The predictins by RGM-H (slid curve), FSS (dashed curve), the Nijmegen HC-F (crsses) and NSC (circles) are displayed. All the mdels give similar results up t 2 Me V / e, except fr sme verestimate f the differential crss sectins in RGM-H. At higher energies, the difference in mdel predictins appears. The 1 PI resnance in HC-F is reflected by the V-shape behavir f the differential crss sectins. The 38 1 resnance in NSC results in very small values f the differential crss sectins fr PE == 4-6 MeV/e. The plarizatin is als sensitive t the resnance structure f the 38 1 phase shift. Fr example, in NSC it stays at small values belw 6 MeV/e. Fr each f these bservables, the tw versins f ur quark mdel predict very similar behavir. We have als cmpared these mdel predictins with the recent experimental data frm KEK fr the E+p differential crss sectins averaged ver the energy range PE = MeV/e. 3) Unfrtunately the pr statistics f the data btained s far preclude any meaningful cnclusin n the phase-shift behavir f the 17+ P interactin in the 3 E and 1 states. Further experimental investigatins f the differential crss sectins and plarizatin at intermediate energies are very imprtant t understand this interactin Ap scattering In this subsectin, we discuss scattering bservables f the Ap interactin based n the analysis f the phase-shift behavir f the AN-EN (I = 1/2) cupled-channel calculatin. It is fund in Ref. 8) that the channel cupling effect between the AN and EN(I = 1/2) channels is very imprtant even belw the EN threshld at PA = 638 MeV /e (which crrespnds t the A-E mass difference dea-e = MeV). This situatin is naturally understd in the quark mdel, since tw 8U3 states, (11)a and (11)8, which newly appear in this system, are largely mixed in the AN system. In particular, the flavr symmetric (11)8 state is cmpletely Pauli frbidden in the mst cmpact (3q)-(3q) cnfiguratin, which yields the strng repulsive frce between the tw (3q) clusters in the 18 state f the EN(I = 1/2) system. On the ther hand, 18 state f the AN system cntains the (22) cmpnent with 9%, resulting in the attractive feature f the phase shift with the shrt-range repulsin, similar t the NN(I = 1) system. The 38 1 states f the AN and EN(I = 1/2) systems bth cntain the (3) and (l1)a cmpnents fifty-fifty, s that ne may expect their interactins t be very similar t each ther s lng as the ttal Hamiltnian is apprximately an 8U3 scalar. It is, hwever, pssible that this bservatin made in Ref. 16) fr the central interactin is largely vilated by the strng effect f the flavr symmetry breaking, especially by the 7r- and K-mesn exchange tensr frce. In the AN system, the ne-pin exchange tensr frce becmes imprtant nly thrugh cupling with the EN channel, whereas it shuld give an appreciable cntributin t the EN system. It is, therefre, imprtant t evaluate the strength f the attractin in each 381 (and als 1 Pt) state f the AN and EN(I = 1/2) systems frm independent experimental surces. Anther characteristic feature f the AN-EN(I = 1/2) system is the (l1)a-(11)8 Dwnladed frm n 24 Nvember 217

16 946 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki 15 r---,----,---,r r----, r---, ~--~ Ph = 2 MeV/c 1 ~ ;:-;:.:-~ Ph = 4 MeV/c RGM-H - FSS -- NSC Jiilich B Ph = 2 MeV/c a Ph = 5 MeV/c 1..5 a ' Ph = 5 MeV/c ~~-+~+==-~-=-~~b=~-+----~--r----~~ Ph = 6 MeV/c 1...,,,,,,,, 5 " L ~ ~~~==~~~===:;==~--~P~h~=--~--~M-e-V-k~--~--~--~ a -1. a c.m. (deg) 8 c.m. (deg) Fig. 7. The differential crss sectins and the deplarizatin fr the Ap system predicted by RGM H (slid curve) and FSS (dashed curve). Partial waves up t J max = 7 are taken int accunt. Predictins by NSC (circles) and Jiilich B (diamnds), which are taken frm Refs. 34) and 6), respectively, are als shwn fr PA = 6 MeV Ie :5 -.5 transitin due t the LS( -) frce. This effect f the flavr-exchange symmetry fr the interchange f the tw particles is accmpanied by the spin transitin between and 1. The spin values are n lnger cnserved in the Y N system, and 1 J J state is cupled t the 3 J J state thrugh the LS( -) frce. Althugh the LS( -) frce exists even in the E+p system, the different SU3 cntent f the 3 and 1 states (which is (22) and (3), respectively) makes the transitin very weak, as lng as the ttal Dwnladed frm n 24 Nvember 217

17 Scattering Observables f the N Nand Y N Interactins Ph = 2 MeV/c Ph = 2 MeV/c " ~ ---: ; ~-~ ~~,.----, -.4 Ph = 4 MeV/c Ph = 4 MeV/c -.4 a: z ~~,..,,--... /' ", ~ " ----:- - /,.",/ ", - /..., ~~, I I " / Ph = 5 MeV/c Ph = 5 MeVlc "" -~ !J._,,"..., ;... " ' ~~ ~ " " ~ " -.2 '~ "... Ph = 6 MeV/c Ph = 6 MeVlc --~ c.m. (deg) 8 c.m. (deg) Fig. 8. The same as Fig. 7, but fr the plarizatin f the scattered (P A ) and recil (P N ) particles. -.4 Hamiltnian is almst an SU3 scalar with a small flavr symmetry breaking. On the ther hand, we have fund in Refs. 7) and 8) that the LS( -) frce riginating frm the Fermi-Breit interactin between quarks plays a very imprtant rle in enhancing the cusp structure f the Ap elastic crss sectins at the EN threshld. This is particularly prminent in the mdel FSS, where the resnance structure in the EN(I = 1/2) 3 PI state is mved t the AN I PI state due t the very strng cupling by the LS( -) frce. We shw belw anther effect f this cupling in the plarizatin bservables. Figures 7 and 8 display the differential crss sectins (da / dd), the deplarizatin Dwnladed frm n 24 Nvember 217

18 948 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki (D), the plarizatin f the scattered (PA) and recil (P N ) particles fr the Ap elastic scattering with respect t varius incident mmenta f the A-particle belw the EN threshld. The slid curve dentes predictins by RGM-H and the dashed curve by FSS. Fr cmparisn, predictins by sme standard OBEP mdels, the Nijmegen NSC and the Jiilich mdel-b (Jiilich B), are indicated by circles and diamnds, respectively. We first nte that the predictins by FSS and RGM-H are very similar, except fr the strnger enhancement f the differential crss sectins in FSS near the EN threshld. This enhancement is apparently related t the fact that the LS( - ) cupling is strnger in FSS than in RGM-H. If we cmpare the predictins f D and PA by varius mdels at PA = 6 MeV Ie, we find that the difference between FSS and RGM-H is smaller than the difference between the tw OBEP mdels. Since predictins f full Wlfenstein parameters by varius OBEP mdels are already given at this particular incident mmentum, we als give ur predictins fr R, R', A and A' in Fig. 9. We find that these quantities are strngly mdel-dependent. Even ur quark mdel predicts different results fr FSS and RGM-H, which is als related t the different cupling features f the AN and EN (I = 1/2) channels by the LS( - ) frce. This difference between FSS and RGM-H smetimes exceeds the difference between the ther tw OBEP mdels. Much experimental infrmatin is required t predict these quantities withut ambiguity. 1. F===~---'-----'--"-----'---I-----r '----'------r-~ RGM-H FSS -- PA = 6 MeV/e NSC JOlieh B 1. f t--r---t---::--:'-...;::---t---t ;i ~..., " """, ' '.. _ : ;---- < ~~~-~~~~,,~-----_~-~t----~~~~~~~o-o-o~d.r'...! " OD:: OC:( _ 1. L--_-L-_----'_-'--...l.-_---". -'--._----L..l...-_--L L-_-L-_---' c-' a c. rn. (deg) a c.rn. (deg) Fig. 9. Wlfenstein parameters R, R', A and A' at PA = 6 MeV Ie. The quark-mdel calculatin by RGM-H (slid curve) and FSS (dashed curve) includes cntributins frm the partial waves up t J max = 7. The predictins by NSC (circles) and Jiilich B (diamnds) are taken frm Refs. 34) and 6), respectively. Dwnladed frm n 24 Nvember 217

19 Scattering Observables f the N Nand Y N Interactins 949 Table II. Ap 1 S and 3 SI phase shifts at PII = 2 MeV Ie and effective range parameters predicted by ur quark mdel, RGM-F, FSS and RGM-H. The crrespnding values predicted by sme OBEP's, the Nijmegen hard-cre mdel-d (HC-D), 2) mdel-f (HC-F), 3) and the sft-cre mdel (NSC) 4) are als shwn fr cmparisn. HC-D HC-F NSC RGM-F FSS RGM-H ISO S as (fm) rs (fm) at (fm) rt (fm) Since the structure f the AN interactin is rather cmplicated, it is necessary t clarify varius aspects f the interactin step by step. First let us discuss the 8-wave phase shifts and their effect n the scattering bservables. Althugh all the mdels fr the Y N interactin are made such that the empirical lw-energy Ap ttal crss sectins in the MeV Ic regin 31), 32) are reprduced, there still remains much ambiguity in the relative strength f the attractin appearing in the 18 and 381 phase shifts. Table II shws the 18 and 381 phase-shift values predicted by varius mdels at PA = 2 MeV Ie, where they reach almst maximum values. The effective-range parameters are als shwn fr cmparisn. These mdels are classified int tw categries; ne gives a small difference between the 18 and 381 phase shifts and the ther gives a larger value fr 18 and a smaller ne fr 3S 1 All the OBEP mdels and RGM-F *) belng t the first categry, and ur new versins f the quark mdel, FSS and RGM-H, belng t the secnd ne. Usually the ISO state is mre attractive than the 381 state, except fr in the Nijmegen mdel-d and RGM-F. This feature is required frm the analysis f the energy spectra f light A hypernuclei. First, the hypertritn ~H is bund, while ~He is nt. Als ;th and ~He have the + grund state and an excited state 1+ at abut 1 MeV. The determinatin f the relative strengths f the attractin in the 1 S and 381 states is, therefre, crucial fr understanding the detailed structure f light A hypernuclei. The tw categries culd be characterized by the deplarizatin D. If we retain nly the 8-wave in the lw-energy limit, D is explicitly calculated frm 2 [(sin6t? + sin6s sin8t cs(8s - 8t )] (3.1) D rv (sin8 s }2 + 3(sin8 t )2 '. where 8 s = 8eS) and 8 t = 8eSI). If 8 s = 8 t, Eq. (3 1) yields D = 1. At PA = 1 MeV Ie, the phase shift values f each mdel give D rv 1 fr the Nijmegen mdel-d and RGM-F, and much smaller values.55 fr FSS and.56 fr RGM-H. ) In Refs. 17) and 18), the K-mesn cupling cnstants, fniik and!nek, fr the tensr term are inadvertently taken t be the electric-type cupling cnstants f the K* mesns; i.e., fniik* = and!nek* =.79199, instead f the crrect values fniik = and!nek = With this change, the 3S1 phase shift f the Ap channel in RGM-F becmes mre attractive than that f the 1 S state. The Ap ttal crss sectin at P II = 2 MeV I e (given in Fig. 14 f Ref. 18)) has increased by abut.i5%, but it is still within the experimental errr bars. The crrect effective range parameters fr the 3 SI phase shift in RGM-F are given in Table II. Dwnladed frm n 24 Nvember 217

20 95 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki Table III. Ap P-wave phase shifts (in degrees) predicted by FSS and RGM-H at energies belw the EN threshld. 3 P, 3 P 2, I Hand 3 PI phase shifts and the mixing angle PI fr I H - 3 PI cupling are listed. PA 3 P 3P 2 IP I 3 PI PI (MeV Ie) FSS RGM-H FSS RGM-H FSS RGM-H FSS RGM-H FSS RGM-H The Nijmegen sft-cre mdel NSC gives.93. The deplarizatin behavir in Fig. 7 clearly shws that this situatin cntinues up t abut 2-3 MeV I e. Once the incident energy becmes higher, the P-wave cntributin becmes imprtant. It is still nt clear if the P-wave AN interactin is repulsive r attractive. The experimental data fr the lw-energy angular distributin seem t indicate that it is slightly attractive, 31),32) althugh these data invlve large errr bars. The central cmpnents in the single-channel P-wave phase shifts f the AN scattering are generally repulsive in ur quark mdel. After intrductin f the nn-central frces, the 3 P phase shift becmes repulsive and the 3 P 2 phase shift becmes attractive, mainly due t the LS frce. Table III shws the P-wave phase shifts f FSS and RGM-H in the full cupled-channel calculatin with respect t the incident mmenta belw the EN threshld. The mixing angles PI between 1 PI and 3 PI channels by the LS( -) frce are als shwn in the standard ntatin f bar phase shifts. Here we clearly find that the mixing is strnger in FSS thari in RGM-H. As the energy appraches the EN threshld, bth f the 1 PI and 3 PI phase shifts exhibit appreciable attractin due t the effect f the step-like 1 PI resnance in FSS and f the dispersin-like resnances in RGM-H. 8) Except fr this quantitative difference f the cupling features near the EN threshld, FSS and RGM-H yield very similar results fr the P-wave phase shifts f the AN elastic scattering. In rder t see the cntributins f the P-wave cmpnents mre clearly, we examine the frward-t-backward rati FIB f the Ap angular distributins fr the energy range PA ~ 3 MeV Ie. If we keep the dminant S-wave phase shifts, 15 s and 15 t, and small crrectins, fl, 15; = 15ept), 15f = 15eP J ) with J =, 1, 2, the ttal differential crss sectins are apprximated by "() "-' [~(sin 15 s )2 + ~ (sin 15t )2] + [~sin 15s sin 15; cs( 15s - 15;) +~ sin 15 t sin 15~ cs(15 t - 15~) + ~ sin 15t sin 15f cs( 15t - 15f) +~ sin15 t sin15; cs(15 t - 15;)] cso. (3 2) Apparently, the attractive feature f the P-wave phase shifts gives an FIB rati Dwnladed frm n 24 Nvember 217

21 Scattering Observables f the N Nand Y N Interactins 951 greater than 1. Nte that the effect f t1 disappears in this apprximatin. We find that F / B = 1.3 (FSS) r 1.4 (RGM-H) fr 1 MeV /c and F/ B = 1.26 (FSS) r 1.33 (RGM-H) fr 2 Me V / c. We cmpare in Fig. 1 the F / B ratis f FSS and RGM-H in the full calculatin with the available experimental data 31),32) fr the energy range up t Eern = 2 MeV (PA rv 316 MeV/e). Our predictin is within the upper limit f the experiment. We can cnclude that the lw-energy P wave Ap interactin is prbably weakly attractive, in accrdance with the phenmenlgical analysis by Dalitz, Herndn and Tang. 33) ~ 1.5 u.. RGM-H - FSS '----'_..5 L--l. 2 -.L 4 ---'s-..l a - '----'-12-1.L4---'1S-1..La---J2 1 E c.m. (MeV) Fig. 1. Frward-t-backward rati f Ap differential crss sectins by RGM-H (slid curve) and FSS (dashed curve) cmpared with the experimental data. 31), 32) This weak attractin riginates frm the cmbined effect f the nn-central frces and the AN-EN(I = 1/2) cupling in ur quark mdel. Anther spin bservable related t the LS( -) frce is the difference between the plarizatin f the scattered A (P A) and the plarizatin f the recil prtn (PN), which is shwn in Fig. 8. This can be seen frm the explicit expressins f these bservables given in Table I f Ref. 23). Since the invariant amplitudes, g and h in Eq. (2 2), vanish fr the elastic scattering, we find '() PnOOO = ~e(a*e + b* J) and '() POnOO = ~e(a*e - b* J). The different signs f f indicate that ne can determine the effect f the LS( -) frce by bserving the difference between PA = PnOOO and?'v = POnOO, since the amplitude f is related t the LS( -) frce. Figure 8 displays the apparent difference between PA and P N bth in FSS and in RGM-H. These bservables are measured experimentally as the left-right asymmetry f the differential crss sectins when the ut -ging A r prtn is rescattered in the target. When the incident mmentum f the A particle exceeds the EN threshld energy 638 Me V / e, charge exchange reactins t EOp and E+ n channels take place. The ttal reactin crss sectins fr Ap -+ EOp are at mst abut 5-6 mb fr bth FSS and RGM-H, as is shwn in Fig. 1(b) f Ref. 8). If we use the isspin relatin fr the scattering amplitudes, the ttal reactin crss sectins fr Ap -+ E+n are twice the abve values. In a subsequent paper,35) we will discuss lw-energy bservables fr E-p scattering, which als invlves the charge exchange reactins t EOn and An channels. 4. Summary A study f the baryn-baryn interactin in the QeD-inspired quark mdel is mtivated t clarify rich lw-energy hadrn phenmena, which result frm the nnperturbative quark dynamics dminated by an effective qq interactin and strng kinematical cnstraints f the quark Pauli principle and symmetries f the spin, flavr and clr degrees f freedm. The mst imprtant findings f such studies Dwnladed frm n 24 Nvember 217

22 952 T. Fujita, Y. Fujiwara, C. Nakamt and Y. Suzuki are the adequacy f the quark degree f freedm in the shrt-range regin and the intricate rle f the mesn-exchange effect in the medium- and lng-range regin. A realistic mdel fr the baryn-baryn interactin with these facets f very different character shuld be examined by cnfrnting the mdel predictins directly with the experimental data. In this paper we have investigated scattering bservables f the N Nand Y N interactins in the lw- and intermediate-energy regin by using a recent quark mdel develped fr the simultaneus descriptin f these interactins. Our mdels, called FSS 7), 8) and RGM-H,8) and their preceding versin RGM-F, 16)-18) are frmulated in the (3q)-(3q) resnating-grup methd (RGM), and incrprate a simple quadratic-type cnfinement ptential, the clr analg f the full Fermi-Breit interactin with explicit quark-mass dependence, and minimum scalar (S) mesn and pseudscalar (PS) mesn effective mesn-exchange ptentials directly cupled t quarks. RGM-F includes nly 7r- and K-mesn tensr frces in additin t the central frce f the full S-mesn nnet, and the spin-flavr-clr factrs f the quarkexchange kernel are apprximately evaluated. On the ther hand, FSS and RGM-H include all the species f the S- and PS-mesn nnets. The spin-flavr-clr factrs f these mesns are explicitly calculated except fr thse f the "isscalar" S-mesns in RGM-H. In this special case, the same apprximatin as is used in RGM-F is emplyed. In FSS and RGM-H, the mdel parameters are determined t fit the N N S-wave and P-wave phase-shift values under the cnstraint f the deutern binding energy and the 1 S scattering length, tgether with the lw-energy Y N "ttal" crss-sectin data. Befre prceeding t the analysis f the Y N scattering bservables, we first examined the quality f ur mdel by calculating the scattering bservables f the np and pp systems, in which the rich knwledge f the phase shifts helps a great deal in understanding the particular rles f the interactin pieces in the scattering bservabies. The energy dependence and the angular-distributin shape f the differential crss sectins, the plarizatin, and sme ther spin bservables are qualitatively reprduced fr the np and pp scattering in a wide energy regin up t abut 3 MeV. Hwever, ur mdels smewhat verestimate the differential crss sectins n the high-energy side. In RGM-F, the lack f the spin-spin term f the PS-mesn exchange ptentials (the ne-pin exchange, in particular) leads t t small values f the np differential crss sectins and the spin crrelatin parameters at backward angles. Thrugh this cmparisn, we can cnfirm that a particular cmpnent f the interactin pieces is strngly reflected in the behavir f sme specific types f spin bservables. After making sure that the discrepancies between the predicted and empirical scattering bservables in the N N system are far smaller than the ambiguity in the present experimental data fr the Y N interactin, we prceeded t study scattering bservables f the Y N systems in FSS and RGM-H. When experimental data are nt available, ur predictins were cmpared with the result f sme OBEP mdels. It is fund that the standard prcedure t crrelate the phase-shift behavir with the scattering bservables is very useful even in the study f the Y N interactin. In the study f E+p scattering we have fund a large mdel-dependence in the Dwnladed frm n 24 Nvember 217

23 Scattering Observables f the N Nand Y N Interactins 953 predicted differential crss sectins and the plarizatin at intermediate energies PI; = 4 ~ 8 MeV/c. The behavir f sme partial waves is strngly reflected in the energy dependence and the angular-distributin shape f the differential crss sectins and the plarizatin. This includes the V-shape angular distributin f the differential crss sectins in the Nijmegen hard-cre mdels 2), 3) thrugh the 1 PI resnance arund P E = 4 Me V / c, and small differential crss sectins in the Nijmegen sft-cre mdel 4 ) and the Jiilich mdels 5), 6) thrugh the 38 1 resnance arund PI; = 4 ~ 6 Me V / c. The differential crss sectins predicted by FSS and RGM-H are very similar, except that RGM-H verestimates the lw-energy crss sectins at PI; :S 2 Me V / c. This similarity is related t the smth energy dependence f the strngly repulsive 38 l phase shift and f the weakly attractive 1 PI phase shift in ur quark mdel. The differential crss sectins at PI; = 45 MeV /c are cmpared t the recent KEK data 3) averaged ver P E = 3 ~ 6 Me V / c. Unfrtunately, rather pr statistics f this experimental data prevent us frm btaining new infrmatin n the E+p interactin in the 3S 1 and 1 PI states. As fr the plarizatin in PI; = 4 ~ 5 MeV /c regin, the Nijmegen mdel-f and the sft-cre mdel give relatively small values, less than.1, while the Jiilich mdels and ur quark mdel yield appreciable values, arund.2. In Ap system we have examined the scattering bservables in the energy range belw the EN threshld (p A = 638 Me V / c). In this system the effect f nn-central frces and the channel-cupling effect between AN and EN(I = 1/2) cnfiguratins are bth very imprtant. The ne-pin tensr frce is respnsible fr the strng cupling amng AN 3S 1, AN 3D 1 and EN(I = 1/2) 3S 1 channels, yielding a prminent cusp structure fr the Ap ttal crss sectins at the EN threshld. Even belw the EN threshld, this tensr cupling is imprtant t make the AN 3S 1 phase shift attractive. Amng many mdels which reprduce lw-energy Ap crss sectins, FSS and RGM-H predict that the lsi state is very attractive and that the 3S state is less attractive. Besides a pssible check f this feature in the energy spectra f s shell A hypernuclei, we have fund that the deplarizatin at lw energies (less than 2 MeV / c) can be used t measure the different strength f attractin between the 1 S and 3 Sl states. In the P-wave interactin, the effect f the LS( ~) frce is very imprtant in ur quark mdel. In particular, FSS gives a strng cupling between 1 PI and 3 PI channels by the LS( ~) frce generated frm the Fermi-Breit interactin, resulting in the strng enhancement f the cusp structure f the Ap ttal crss sectins in the EN threshld regin. The effect f this cupling cntinues dwn t energies f abut 4 MeV/c. By examining the frward-t-backward rati F / B f the differential crss sectins, we find that the lw-energy P-wave Ap interactin at PA :S 3 MeV /c is weakly attractive due t the cmbined effect f the LS and LS(~) frces, and f the AN-EN(I =: 1/2) channel cupling. As a direct detectin f the LS( ~) frce, we have pinted ut that the scattered A-particle and the recil prtn have the plarizatin f almst ppsite signs at intermediate energies. The Wlfenstein parameters at PA = 6 MeV /c were als calculated in FSS and RGM-H. Because f the quantitative difference in the strength f the AN-EN(I = 1/2) cupling, the tw mdels give a sizable discrepancy fr the predicted values, which is cmparable t that between ther OBEP mdels. This indicates that mre exper- Dwnladed frm n 24 Nvember 217