Strangeness Strangeness S=- S=- baryon-baryon baryon-baryon interactions interactions from from Lattice Lattice QCD QCD Kenji Sasaki YITP, Kyoto University for HAL QCD Collaboration H HA ALL H Hadrons adrons to to A Atomic tomic nuclei nuclei from from LLattice attice QCD QCD Collaboration Collaboration S. Aoki YITP T. Doi RIKEN F. Etminan Birjand U. S. Gongyo U. of Tours T. Hatsuda RIKEN Y. Ikeda RCNP T. Inoue Nihon U. N. Ishii RCNP T. Iritani RIKEN D. Kawai YITP T. Miyamoto YITP K. Murano RCNP H. Nemura U. of Tsukuba
Introduction Introduction BB interactions are crucial to investigate the nuclear phenomena Once we obtain proper nuclear potentials, we apply them to the structure of hyper- nucleus. BB BB interaction interaction potential potential u ds uu d Properties of nuclaer potential State dependence spin, isospin Long range attraction Short range repulsion How do we obtain the nuclear force?
Derivation Derivation of of hadronic hadronic interaction interaction from from QCD QCD Start Start with with the the fundamental fundamental theory,qcd theory,qcd Lattice Lattice QCD QCD simulation simulation Lüscher's Lüscher's finite finite volume volume method method M. Lüscher, NPB3549953 u ds. Measure the discrete energy spectrum, E uu d. Put the E into the formula which connects E and δ E 00tt t t00 E 0 B 0 BBBt t,, r rb B B B t t00 0 = 0 =AA00Ψ Ψ r r,, EE00e e + + Scattering Scattering phase phase shift shift HAL HAL QCD QCD method method Ishii, Aoki, Hatsuda, PRL99 007 000. Measure the NBS wave function, Ψ. Calculate potential, V, through Schrödinger eq. 3. Calculate observables by scattering theory Guaranteed to be the same result T. Kurth et al JHEP 3 03 05 T. IritaniHAL QCD Lattice05
HAL HAL QCD QCD method method NBS NBS wave wave function function Et t 0 Ψ E, r e = 0 Bi t, x + r B j t, x E, t 0 ΨE, r A x E : Total energy of system In asymptotic region : p + Ψ E, r =0 sin pr + δe pr Aoki, Hatsuda, Ishii, PTP3, 89 00. In interaction region : p + Ψ E, r =K E, r B B RI Modified Modified Schrödinger Schrödinger equation equation m+ mt t, r =Ψ B B r, t e B B B B 3 + R I t, r = U r, r ' R I t, r d r ' t μ N. Ishii et al Phys. Lett. B70437 Derivative Derivative expansion expansion U r, r ' = V C r + S V T r + L S s V LS r + L S a V ALS r+o K. Murano et al Phys.Lett. B735 04 9 Potential Potential B B B B V r = + R I t, r / R I t, r t μ
HAL HAL QCD QCD method method coupled-channel coupled-channel NBS NBS wave wave function function Ei t Ψ E i, r e = 0 B B r E i E t Ψ E i, r e = 0 B B r E i i dr Ψ E ', r Ψ γe, r =δe ' E δ γ B B R E t, r =Ψ B B r, E e E + m+ mt Leading order of velocity expansion and time-derivative method. Modified Modified coupled-channel coupled-channel Schrödinger Schrödinger equation equation + R E t, r V r V r Δ t R E t, r t μ = V r Δ t V r R t, r R E t, r E + R E t, r + V r V r Δ t R E t, r t μ t μ = exp m + m t Δ = V r Δ t V r R r E t, exp m + m t + R E t, r t μ 0 0 0 0 S.Aoki et al [HAL QCD Collab.] Proc. Jpn. Acad., Ser. B, 87 509 K.Sasaki et al [HAL QCD Collab.] PTEP no 05 3B0 Potential Potential Considering two different energy eigen states V r V r Δ V r Δ V r R E0 t, r R E t, r μ t μ t R E0 t, r R E t, r = R E0 t, r R E t, r R t, r R t, r μ t E0 μ t E
Introduction Introduction BB interactions are crucial to investigate hyper-nuclear structures Lattice Lattice QCD QCD simulation simulation S=-6 S=-6 S=-5 S=-5 Advantageous Advantageous for for more more strange strange quarks quarks Signals Signals getting getting worse worse as as increasing increasing the the number number of of light light quarks. quarks. Complementary Complementary role role to to experiment. experiment. Main Main topics topics of of S=- S=- multi multi baryon baryon system system H-dibaryon H-dibaryon S=-4 S=-4 R.L. R.L. Jaffe, Jaffe, PRL PRL 38 38 977 977 95 95 Double-L Double-L hypernuclei hypernuclei Strangeness S=-3 S=-3 K.Nakazawa K.Nakazawa et et al, al, KEK-E76 KEK-E76 Collaboration Collaboration X-hypernuclei X-hypernuclei S=- S=- K.Nakazawa K.Nakazawa et et al, al, KEK-E373 KEK-E373 Collaboration Collaboration S=- S=- Experiment Experiment S= S= 00 J-PARC
Baryon-baryon Baryon-baryon system system with with S=- S=- Spin Spin singlet singlet states states Isospin I=0 Spin Spin triplet triplet states states BB channels N I= I= Isospin --- N LS -- I=0 I= BB channels -L N N -SS Relations Relations between between BB BB channels channels and and SU3 SU3 irreducible irreducible representations representations 88 xx 88 == 7 7 ++ 88SS++ ++ 0 0 ++ 0 0 ++ 88AA JJpp=0 =0++,, I=0 I=0 5 8 ΛΛ NΞ = 0 8 40 ΣΣ 5 4 JJpp=0 =0++,, I= I= N Ξ = ΣΛ 5 3 7 3 8 7 8 7 JJpp=0 =0++,, I= I= Σ Σ 8 JJpp= =++,, I=0 I=0 N Ξ 8 JJpp= =++,, I= I= NΞ Σ Λ = 6 3 3 ΣΣ 8 0 4 0 0 Features of flavor singlet interaction is integrated into the S=- Jp=0+, I=0 system.
Keys Keys to to understand understand H-dibaryon H-dibaryon A strongly bound state predicted by Jaffe in 977 using MIT bag model. H-dibaryon H-dibaryon state state is is SU3 SU3 flavor flavor singlet singlet [uuddss], [uuddss], strangeness strangeness S=-. S=-. spin spin and and isospin isospin equals equals to to zero, zero, and and JJPP== 00++ Strongly attractive interaction is expected in flavor singlet channel. Short range one-gluon exchange contributions Strongly attractive Color Magnetic Interaction Symmetry of two-baryon system Pauli principle Flavor singlet channel is free from Pauli blocking effect Pauli 7 mixed 8 forbidden allowed 0 mixed 0 forbidden 8 mixed CMI repulsive repulsive attractive repulsive repulsive repulsive Oka, Shimizu and Yazaki NPA464 987
Hunting Hunting for for H-dibaryon H-dibaryon in in SU3 SU3 limit limit Strongly attractive interaction is expected in flavor singlet channel. Strongly attractive potential was found in the flavor singlet channel. Bound state was found in this mass range with SU3 symmetry. T.Inoue et al[hal QCD Coll.] NPA880 8 What happens at the physical point? SU3 breaking effects Threshold separation Changes of interactions Non-trivial contributions
Works Works on on H-dibaryon H-dibaryon state state Theoretical Theoretical status status P. E. Shanahan et al PRL 070 09004 Several sort of calculations and results bag models, NRQM, Quenched LQCD. There There were were no no conclusive conclusive result. result. Chiral extrapolations of recent LQCD data Y.Yamaguchi and T.Hyodo hep-ph:607.04053 Unbound or resonance Experimental Experimental status status NAGARA Event K.Nakazawa et al KEK-E76 & E373 Coll. PRL8700 50 Deeply bound dibaryon state is ruled out CK-,K+LL reaction C.J.Yoon et al KEK-PS E5 Coll. YS and YS decays B.H. Kim et al Belle Coll. PRC75007 00R PRL003 00 Significance of enhancements below 30 MeV. Larger statistics J-PARC E4 There is no sign of near threshold enhancement.
Numerical Numerical setup setup + flavor gauge configurations. Iwasaki gauge action & Oa improved Wilson quark action a = 0.086 [fm], a =.300 GeV. 963x96 lattice, L = 8.4 [fm]. 44 confs x 8 sources x 4 rotations. Flat wall source is considered to produce S-wave B-B state. Mass [MeV] p K mp/mk N 46 55 0.8 L 956± ±4 S 0±3 X 38±3 8MeV 9MeV 7MeV 4MeV Kenji Sasaki YITP Kyoto University for HAL QCD collaboration
LL, NX I=0 S00 potential potential ch ch calc. calc. LL, NX I=0 S Nf = + full QCD with L = 8fm, mp = 46 MeV LL-LL LL-LL Potential calculated by only using LL and NX channels. Long range part of potential is almost stable against the time slice. Short range part of NX potential changes as time t goes. LL-NX transition potential is quite small in r > 0.7fm region Preliminary! LL-NX LL-NX NX-NX NX-NX
LL and NX phase shift shift and and inelasticity inelasticity LL and NX phase Nf = + full QCD with L = 8fm, mp = 46 MeV LL LL phase phase shift shift Inelasticity Inelasticity LL and NX phase shift is calculated by using ch effective potential. A sharp resonance is found just below the NX threshold. Inelasticity is small. NX NX phase phase shift shift t=09 t=09 t=0 t=0 t= t= Preliminary!
Breit-Wigner Breit-Wigner mass mass and and width width Nf = + full QCD with L = 8fm, mp = 46 MeV Preliminary! Fitting the time delay of LL scattering by the Breit-Wigner type finction, LL LL phase phase shift shift Resonance Resonance enargy enargy and and width width t=09 t=09 Time Time delay delay E R E Λ Λ =4.894±0.039[ MeV ] Γ = 0.099±0.059[ MeV ] t=0 t=0 In the vicinity of resonance point, δ E =δ B arctan thus Γ/ E E r d δ E Γ/ = de E E r + Γ/ E R E Λ Λ =4.97±0.056[ MeV ] Γ = 0.077±0.0[ MeV ] t= t= E R E Λ Λ =4.97±0.05[ MeV ] Γ = 0.050±0.053[ MeV ] Kenji Sasaki YITP Kyoto University for HAL QCD collaboration
Summary Summary H-dibaryon state is investigated using 44confs x 8src x 4rot. We perform LL-NX coupled channel calculation. Sharp resonance is found just below the NX threshold. Resonance position and width from Breit-Wigner type fit Preliminary! We continue to study it by using higher statistical data. Kenji Sasaki YITP Kyoto University for HAL QCD collaboration