Hyperon interactions & H-dibaryon from recent Lattice QCD Simulation. Takashi Inoue, Nihon Univ. HAL QCD Collaboration

Transcription

1 Hyperon interactions & H-dibaryon from recent Lattice QCD Simulation Takashi Inoue, Nihon Univ. HAL QCD Collaboration S. Aoki T. Doi T. Hatsuda Y. Ikeda T. Inoue N. Ishii K. Murano H. Nemura K. Sasaki Univ. Tsukuba Univ. Tokyo RIKEN Tokyo Inst. Tech. Nihon Univ. Univ. Tsukuba RIKEN Tohoku Univ. Univ. Tsukuba Crossover, June 23, 2011

2 Plan Introduction Setup Action & facility, Operator & source, Hadron masses Results purpose & goal, key points of this study, strategy H-dibaryon Hyperon interactions Summary & Outlook

3 Introduction Hyperon interaction (YN, YY int.) are important for neutron-star, super-nova phys. and so on. however, are not well known due to lack of experimental data. H-dibaryon: predicted compact 6-quark state (not found) Flavor singlet, No Pauli exclusion, Attractive OGE-contr. Our purpose and goal R. L. Jaff, Phys. Rev. Lett. 38(1977) 1. We reveal BB int. directly from QCD using lattice simulation, including (un)existence of the H-dibaryon. 2. We get deeper understanding of BB int. 3. People can apply them to many physics (super-nova etc). Now, we are at middle of the 2nd stage. T. Inoue et. al. Phys. Rev. Lett. 106, (2011) T. Inoue et. al. Prog. Theo. Phys. Vol. 124, No. 4 (2010) 591 Two keys of these study: We utilize a very useful tool that is the interaction potential. We consider the flavor SU(3) limit world. 3

4 Why flavor SU(3) limit In the limit, convenient basis exist to describe the int. 8 8 = s * a flavor irreducible rep. Symmetric In S-wave, no off-diagonal interaction exists. 1 S 0 : V (27) (r), V (8s) (r), V (1) (r) Fermi statistics leads to Anti-symmetric 3 S1 : V (10 *) (r), V (10) (r), V (8a) (r) V(a) contain essential flavor-spin structure of BB int. We can reconstruct all baryon-base interaction (eg. ΛN) by using these V(a)(r) with SU(3) C.G. coefficients. V(a) are useful to pin down physical origin of a particular feature, since effective models assume flavor symmetry. 4

5 Hadron system from LQCD Conventional use energy eigenstate (eigenvalue) Lüscher's finite volume method for phase-shift Infinite volume extrapolation to get bound state energy HAL use the potential V(r) +... from the NBS w.f. Solve the effective theory which reproduce T matrix of QCD Advantages No need to separate E eigenstate Only need to measure NBS w.f. Demand a minimal lattice volume Can produce more observables Nee to check validity of the leading term V(r) Example of such study 5

6 Difficulty in conventional approach saturation OK saturation NG Left: On L = 2 [fm], NBS w.f. doesn't change as t at t 10. Right: On L = 4 [fm], NBS w.f. does change as t at t 10. Cause is K nx, ny, nz = (n2x +n 2y +n2z ) 55 [MeV] Bigger L makes Exp tail apparent. Need to take larger t. But, t is limited. And, at larger t, S/N becomes rapidly bad. It is practically impossible to get G.S.S. on L =4 [fm] lattice. (as far as we use one source) 6

7 New method N. Ishii etal. [HAL QCD coll.] in preparation EGr t NBS wave function ψ( r,t) = ϕgr ( r ) e E1st t + ϕ1st ( r ) e Euclidian space-time Schrödinger eq. of energy-eigen-w.f. [ [ 2 ] ] [ E t 3 E 2MB ϕgr ( r )e + d r ' U ( r, r ') ϕgr ( r ' )e 2μ Gr 2 E 2 MB ϕ1st ( r )e 2μ By adding equations 1st t 3 + d r ' U ( r, r ') ϕ1st ( r ' )e t = E Gr ϕgr ( r )e E1st t = E 1st ϕ1st ( r ) e Gr EGr t E 1st t Non-local but energy independent ] 2 d 3 2 MB ψ( r, t) + d r ' U ( r, r ' )ψ( r ', t) = ψ( r, t) 2μ dt expansion U ( r, r ') = V ( r, )δ( r r ') = [V ( r ) ]δ( r r ' ) & truncation d ψ( r,t) 2 Therefor, in 1 ψ( r, t) dt V ( r ) = 2MB the leading 2μ ψ( r,t) ψ( r,t ) must be t-indep. (non-trivial) t-derivative at each r different from previous method 7

8 Set up 8

9 Lattice & action & facility β 1.83 a [fm] 0.121(2) Lattice 323 x 32 L [fm] 3.87 Renormalization group improved Iwasaki gauge and Non-perturbatively O(a) improved Wilson quark We thank K.-I. Ishikawa and the PACS-CS group for providing their DDHMC/PHMC code to generate gauge configuration, and the Columbia Physics System for their lattice QCD simulation code. We enhance S/N of data by averaging on 4x4=16 source, and forward/backward propagation in time. We've carried out all numerical computation at the supercomputer system T2K-Tsukuba. 9

10 Operator & source NBS w.f. the same ψ ( r, t) = 0 B i ( x + r,t ) B j ( x, t) B=2,a-plet (a) x = G ( x + r, x, t ) (a) with the 4-point function x (a) (a) G ( x, y, t t 0 ) = 0 Bi ( x,t ) B j ( y,t ) BB (t 0 ) 0 Point type octet baryon field operator at sink p α (x ) = ϵ c c c (C γ5 )β β δβ α u(ξ1 )d (ξ2 )u(ξ3 ) Λα ( x) = ϵ c c c (C γ5 )β β δβ α with ξ i={c i, βi, x } 1 [ d (ξ1) s(ξ2)u(ξ3)+s(ξ1)u(ξ2 )d(ξ3 ) 2u(ξ1)d (ξ2) s(ξ3)] 6 Quark wall type source for BB in the flavor irreducible rep. e.g for flavor-singlet BB (1) = ΛΛ + ΣΣ + ΝΞ

11 Hadron masses K_uds N_cfg M_P.S. [MeV] M_Vec [MeV] M_Bar [MeV] (7) (0.9) 2274(2) (6) (1.1) 2031(2) (5) (0.9) 1749(1) (6) (1.0) 1484(2) (8) 830.6(1.5) 1163(2) To date, 5 simulations at different hopping parameter (quark mass) With lightest quark (bottom row of the table), p.s. meson is lighter than physical kaon. baryon is lighter than physical sigma baryon. Now, simulated hadron world is similar to the real world, although SU(3) breaking is not taken into account. 11

12 Results 12

13 Potential V S0 (a) Kuds= S1 3 D1 u+d u+d+s 3 We see strong flavor-spin dependence in the flavor rep. base. We see variety of BB interaction in the u,d,s 3-flavor world. This shows that quark model predictions are surprisingly correct.13

14 Potential V S0 (a) Kuds= S1 3 D1 u+d u+d+s 3 We see strong flavor-spin dependence in the flavor rep. base. We see variety of BB interaction in the u,d,s 3-flavor world. This shows that quark model predictions are surprisingly correct.14

15 H-dibaryon 15

16 NBS w.f. & potential Left: the NBS w.f. of the flavor singlet channel The cause for it doesn't go to zero, is a excited states contribution as well as a finite volume effect. (demonstrated in later) Right: the potential of the flavor singlet channel V(1)(r) become strong as quark mass decrease. 16

17 Observables Preliminary Left: the scattering phase shift v.s. Ecm Right: the ground state in the infinite volume which is MeV lower than a free BB ie. 3q-3q. This means that there is a 6-quark bound state in the f-singlet. A stable(bound) H-dibaryon exists in these SU(3)F limit world! 17

18 Wave functions from V (1) Left: w.f. of the lowest two states in the flavor singlet Obtained from the effective theory of QCD involving V(1)(r) Right: comparison to the deuteron w.f. Obtained from the modern realistic NN potential AV18 One can get feeling of H-dibaryon. 18

19 Anti-symmetric flavor octet (8a) Left: Quark mass dependence of the potential V (8a). V(8a) is less repulsive at short distance with heavier quark. Right: S-wave phase-shift in BB 8a-plet ch. A weakly bound state appear at between Mps = [MeV]. But, discretization effect may be large at heavy quark mass. We need more careful study. 19 QCM study in e.g. M. Oka, Phys. Rev. D38 (1988) 298

20 Hyperon interaction 20

21 Potential in baryon-base In flavor SU(3) broken world, e.g. the physical one, the baryon-basis are used instead of flavor-basis. In the SU(3) limit, the baryon-base potential Vij(r) can be obtained by a unitary rotation of the potential V(a)(r). e.g. S= 2, I=0 sector Λ Λ ( ) Σ Σ = Ξ N ( ) ( 27 U 8, 1 U coupled channel V (27) ) ( = U (1) t V (8) V V Λ Λ V ΛΣΛΣ V ΛΞΛN V Σ Σ V ΣΞΣN ΞN V ) I show you potentials Vij(r) at the lightest quark mass (Kuds = , Mps=469 MeV) obtained with V(a) in an analytic function fitted to data. 21

22 Uncoupled (exclusive) channels Some BB channels belong to a flavor irr-rep. exclusively. Potential of such BB channel is nothing but V(a)(r). S=0 and S= 4 BB channels are completely exclusive. Large uncertainty 22

23 S= 1, I=1/2 sector NΛ - NΣ(I=1/2) coupled. 1S0 VNΛ has attractive well. VNΣ is strongly repulsive. JP = 1+ Both have an attractive well. NΛ - NΣ strongly coupled. Off-diagonal VT is stronger. 23

24 S= 2, I=0 sector ΛΛ ΝΞ ΣΣ coupled. Left: diagonal. Right: Off-diagonal. It is flavor symmetric(spin singlet), and involve flavor singlet ch. Channel coupling int. are comparable to diagonal ones, except for the ΛΛ - ΝΞ transition (small sign change in VΛΛ-ΝΞ must be artifact). Interaction is most attractive in NΞ channel, although it has not much real meaning because channel coupling is strong. 24

25 S= 2, I=1 sector ΝΞ ΣΛ ( ΣΣ) coupled. 1S0 VNΞ VΣΛ, moderate coupling JP = 1+ Need to solve 6-channel-coupled Schrödinger eq. for observables. 25

26 S= 3, I=1/2 sector ΛΞ ΣΞ coupled. 1S0 VΛΞ = VΛN, VΣΞ = VΣN JP=1+ strong channel coupling by VC. hyperon-changing VT vanishs. 26

27 Summary I've introduced our motivation, purpose and goal. I've explained two keys of this study. reveal BB interactions directly from QCD using lattice investigate flavor SU(3) limit to capture essential physics extract potentials from NBS, as a convenient tool/concept. I've shown strongly flavor-spin dependent various S-wave BB int. that quark model predictions are surprisingly correct. This indicates importance of the Pauli exclusion at small r. that a bound=stable H-dibaryon exists in SU(3)F limit world. EB = MeV depend on quark mass. Size is compact. all of S-wave NN, YN and YY interaction potentials Vij(r). coupled channel in the baryon basis, VC and VT 27

28 Outlook I'll study H-dibaryon at as many (mπ, mk) points as possible. We'll deeply understand BB int. e.g. physical origin of features, by comparing LQCD results to models. Many application. Many other ongoing studies NN int. in higher partial wave by N. Ishii, K. Murano YN, YY int. with SU(3)F breaking by H. Nemura, K. Sasaki Three nucleon force by T. Doi Meson-baryon (KN) int. by Y. Ikeda 28

29 Thank You! 29