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Quark-model baryon-baryon interactions and their applications to few-body systems

Quark-model baryon-baryon interactions and their applications to few-body systems. Y. Fujiwara （ Kyoto) Y. Suzuki （ Niigata ） C. Nakamoto (Suzuka) M. Kohno （ Kyushu Dental ） K. Miyagawa （ Okayama) 1. Introduction

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Quark-model baryon-baryon interactions and their applications to few-body systems

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  1. Quark-model baryon-baryon interactions and their applications to few-body systems Y. Fujiwara （Kyoto) Y. Suzuki （Niigata） C. Nakamoto (Suzuka) M. Kohno（Kyushu Dental） K. Miyagawa（Okayama) 1. Introduction 2. B8B8 interactions fss2 and FSS: spin-flavor SU6 symmetry 3. B8 interactions by quark-model G-matrix 4. Some applications 4.1. N interaction and 3H Faddeev calculation 4.2 effective  potential and 9Be Faddeev calculation 4.3.  s. p. potential and  , (3N) potentials 4.4. N total cross sections and  potential 5. Summary 2006.10.13 HYP2006 Mainz

  2. 6 i=1 ∑ ∑ 6 i<j Oka – Yazaki (1980)  Phys. Rev. C64 (2001) 054001 Phys. Rev. C65 (2002) 014001 B8B8 interactions by fss2 • Short-range repulsion and LS by quarks • Medium-attraction and long-rang tensor byS,PSandV • meson exchange potentials (fss2) (Cf. FSS withoutV) Phys. Rev. C54 (1996) 2180 Model Hamiltonian Anatural and accurate description of NN, YN, YY interactions in terms of (3q)-(3q) RGM H = (mi+pi2/2mi) + +(UijConf+UijFB+∑βUijSβ +∑βUijPSβ + ∑βUijVβ) f(3q)f(3q)|E-H|A {f(3q)f(3q)c(r)}=0 PPNP in press Arndt : SAID Nijmegen : NN-OnLine QMPACK homepagehttp://qmpack.homelinux.com/~qmpack/index.php 2006.10.13 HYP2006 Mainz

  3. P.T.P. 103 (2000) 755 Lippmann-Schwinger (LS) RGM Solve [ - H0 - VRGM() ] =0withVRGM()=VD+G+ K in the mom. representation ( = E - Eint ) Born kernel qf|VRGM() |qi  T-matrix, G-matrix 1) non-local 2) energy-dependent 3) Pauli-forbidden states in N - N (I=1/2),  - N -  (I=0),  -  (I=1/2) 1S0 : i.e. SU3 (11)s : Ku=u 3-cluster Faddeev formalism using VRGM() P.T.P. 107 (2002) 745; 993 self-consistency equation for 

  4. B8 interaction by quark-model G-matrix  : “(0s)4” =0.257 fm-2 G (p, p’; K, , kF) B8 relative q’ k’=p’- p , q’=(p+p’)/2 incident q1 G (k’,q’; q1, q’) in total c. m.  - cluster folding kF=1.35 fm-1 k=k’ q1=qfor direct and knock-on V (k, q) VW (R, q) : Wigner transform k=pf - pi , q=(pf+pi)/2 V (pf , pi) U(R)=VW(R, (h2/2)(E-U(R)) Transcendental equation Lippmann - Schwinger equation Schrödinger equation exact EB ,  (E) EBW , W(E) 2006.10.13 HYP2006 Mainz

  5. “constant K , , kF” q1=0 q’=3/5 kF kF=1.35fm-1 n RGM by G-matrix of fss2 n sactt. phase shift S1/2 P3/2 P1/2 exp 2006.10.13 HYP2006 Mainz

  6. S B8B8(I) 1E, 3O (P =symmetric) 3E, 1O (P =antisymmetric) NN(0) NN(1) ― (22) (03) ― ‐1 LN SN(1/2) SN(3/2) [(11)s+3(22)] [3(11)s‐(22)] (22) [‐(11)a+(03)] [(11)a+(03)] (30) LL XN(0) XN(1) SL SS(0) SS(1) SS(2) (11)s+ (22)+ (00) (11)s‐ (22)+ (00) (11)s+ (22) ｰ (11)s+ (22) (11)s－ 　　 (22)－ (00) ― (22) ― (11)a [‐(11)a+ (30)+(03)] [(30)‐(03)] ― [2(11)a+ (30)+(03)] ― ‐3 XL XS(1/2) XS(3/2) [(11)s+3(22)] [3(11)s‐（22）] (22) [‐(11)a+(30)] [(11)a+(30)] (03) XX(0) XX(1) ― (22) (30) ― B8B8 systems classified in the SU3 states with (l, m) 0 ‐2 ‐4 (30)almost forbidden (m=2/9) (11)scomplete Pauli forbidden

  7. Spin-flavor SU6 symmetry 1. Quark-model Hamiltonian is approximately SU3 scalar ・ no confinement contribution (assumption) 　　・ Fermi-Breit int. … quark-mass dependence only 　 ・ EMEP … automatic SU3 relations for coupling constants phenomenologyCf. OBEP: exp data  g, f,  … (integrated) 2. -on plays an important role through SU3 relations and FSB 3. effect of the flavor symm. breaking (FSB) by ms>mud , B, M masses Characteristics of SU3 channels

  8. 1S0 phase shifts for B8B8 interactions with the pure (22) state (fss2) S=‐2 1S0 S=0 S=‐3 S=‐1 (22) S=‐4 effect of FSB is very large

  9. 3S1 phase shifts NN fss2 3S1 (03) NN (03) central only (no  tensor) (3/2) (11)a (11)a : weakly attractive N (0)  (0) (30) N (3/2) (30) : Pauli repulsion

  10. +p differential cross sectionsand +p, pasymmetries a() Ahnet al.(KEK-PS E251, E289) NP A648(1999)263, A761(2005)41 Kurosawa et al. (KEK-PS E452B) KEK preprint 2005-104 (2006) 350 MeV/c  plab 750 MeV/c +p +p elastic aexp=0.44±0.2 at p=800±200 MeV/c reported by K. Nakai p elastic Kadowaki et al.(KEK-PS E452) Euro. Phys. J. A15 (2002) 295

  11. N interaction by fss2 Backward/Forward ratio P-wave N is weakly attractive FSS fss2  from3HeFaddeev N -Ncoupling :3S1 +3D1by one- tensor 1P1+3P1by FB LS (－)

  12. u s u d d d ed=2.22 MeV BΛ=130 ±50 keV 3H (hypertriton) NN-NN CC Faddeev Phys. Rev. C70, 024001 (2004) N on-shell properties are directly reflected 1S0 / 3S1 relative strength “ｄｅｕｔｅｒｏｎ” Λ(∑0 ) exp’t u u ~5 fm d p P (%) ~2 fm close to NSC89 fss2 289 keV 0.80 FSS 878 keV 1.36 n eNN= 19.37 – 21.03 = －1.66 |eｄ|= 17.50 – 19.72 = －2.22 (MeV) 150 channel calculation

  13. N １Ｓ0ａｎｄ３Ｓ１effective range parameters “fss2”: m c2 = 936 MeV  1,000 MeV favorable for 4H (1+) Effect of the higher partial waves is large 90 – 60 keV vs. 20 – 30 keV in NSC89 BΛexp=130 ±50 keV

  14.  effective local potentials by G-matrix B8B8 interaction effective potentials quark-model N-N ND EB (exact) －3.62 MeV －3.18 MeV EBexp=3.120.02 MeV Cf. U(0)＝‐46 (FSS), ‐48 (fss2) MeV in symmetric matter

  15. (3.04 MeV) 2+ 2 Faddeev for 9Be Phys. Rev. C70, 024002, 0407002 (2004) (0) 92 keV 0+  + + 8Be  RGM kernel (MN3R) effective  pot. (SB u=0.98) exp’t -3.120.02 MeV 3067(3) keV 3026 keV 3/2+ +5He 5/2+ 3024(3) keV 2828 keV -6.620.04 MeV 1/2+ calc. 9Be  s splitting byN LS Born kernel 198 keV (fss2 quark+), 137 keV (FSS) : 3  5 times too large Eexp(3/2+ - 5/2+) = 43  5 keV Akikawa, Tamura et al. (BNL E930) Phys. Rev. Let. 88, 082501 (2002)

  16. s splitting of9Beby2 Faddeev using quark-model G-matrix  LS Born kernel FSS (cont) reproduces E exp at kF=1.25 fm-1 ! P-wave N-N coupling by LS(-) is important. S-meson LS in fss2 is not favorable.

  17.  potentials (VWC (R, 0)) by quark-model G-matrix interaction FSS fss2 I=3/2 I=3/2 total total I=1/2 I=1/2 The Pauli repulsion of N(I=3/2) 3S1 is very strong.

  18.  (3N) potentials by quark-model G-matrix interaction ( 0+, T=1/2 channel) (3N): (0s)3 =0.22 fm-2 q1=0 FSS fss2 EB(exact)＝－3.79 MeV EB(exact)＝－5.70 MeV consistent with 4He (0+) resonance

  19. （－, K+)inclusive spectra on28Si exp: Noumi et al. PRL 89, 072301 (2002) ; 90, 049902 (E) (2003) Saha et al. Phys. Rev. C70, 044613 (2004) poster session by M. Kohno Repulsive U (q) in symmetric nuclear matter is experimentally confirmed.

  20.  potentials (VWC (R, 0)) by quark-model G-matrix interaction FSS fss2 I=1 I=1 total total I=0 I=0 Some attraction in the surface region.

  21. +3.7 -3.6 Tamagawa et al.(BNL-E906) Nucl. Phys. A691 (2001) 234c Yamamoto et al. Prog. Theor. Phys. 106 (2001)363 - (in medium) = 30.7±6.7 mb (eikonal approx.)= 20.9±4.5 mb +2.5 -2.4 +1.4+0.7 -0.7 -0.4 -p /-n =1.1 at plab=550 MeV/c   FSS fss2 Ahn et al. Phys. Lett. B 633 (2006) 214   More experiments are needed.

  22. Ｓｕｍｍａｒｙ Quark-model description for the baryon-baryon interaction is very successful to reproduce many experimental data. In particular, the extension of the (3q)-(3q) RGM study for the NN and YN interactions to the strangeness S=-2, -3, -4 sectors has clarified characteristic features of the B8B8 interactions. The results seem to be reasonable if we consider 1)spin-flavor SU6 symmetry 2) weak π-on effect in the strangeness sector 3) effect of the flavor symmetry breaking We have analyzed B8, B8(3N) interactions based on the G-matrix calculations of fss2 and FSS.

  23. Characteristics of fss2 and FSS S=0 ・ triton binding energy … fss2: +150 keV (3 body force?) S＝‐1 pand+pinteractions are progressively known. ・ +p total and differential cross sections and polarization … fss2, FSS ・ N1S0 and 3S1 attraction (relative strength) ( 3H Faddeev calculation: 289 keV for fss2) ・ small s splitting in 9Beexcited states(FSS) ・ N (I=1/2 1S0), N (I=3/2 3S1) repulsion  repulsive s. p. and  potentials … fss2, FSS S＝‐2  interaction is not much attractive ! ・  interaction |V|<|VN|<|VNN| B  1 MeV (Nagara event 6He) … fss2 ・ N in-medium total cross section (fss2, FSS) … strong isospin dependence of  s.p. potential ・ N (I=0 3S1): (11)a  0 or weakly attractive (fss2, FSS) vs. ESC04(d): strongly attractive

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