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Multi-Strangeness Dibaryon

Multi-Strangeness Dibaryon. T.Goldman, TD, LANL Y.X.Liu, Peking Univ. X.F.Lu, Sichuan Univ. J.L.Ping, Nanjing Normal Univ. Fan Wang, Nanjing Univ. Contents. “Discovery” of multi-quark states. Candidates of multi-strangeness dibaryons. RHIC is a factory of multi-quark.

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Multi-Strangeness Dibaryon

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  1. Multi-Strangeness Dibaryon T.Goldman, TD, LANL Y.X.Liu, Peking Univ. X.F.Lu, Sichuan Univ. J.L.Ping, Nanjing Normal Univ. Fan Wang, Nanjing Univ.

  2. Contents • “Discovery” of multi-quark states. • Candidates of multi-strangeness dibaryons. • RHIC is a factory of multi-quark. • Nonperturbative QCD basis of quark models. • Proposal

  3. “Discovery” of Multiquark The “discovery” of multiquark states sets challenges as well as opportunities to quark models. Eleven groups claimed that they observed a penta quark state, called Θ+: Θ+: I=0, J=1/2, Parity=?, M=1540MeV, Γ≤25MeV, NA49 Ξ--: I=3/2, M=1862MeV, Γ≤ 18MeV, H1 Θc : I=0, M=3099 MeV, Four groups clamed that they observed tetra quark states . Up to now no dibaryon or hexa quark state has been observed . • If the Pendora box of multi quark really has been opened, all of these multiquark states should appear sooner or later. The discovery of multi-quark states sets challenges as well as opportunities to quark models, even lattice QCD and others. Four lattice QCD calculations gave totally different results. There have been more than 200 papers about pentaquark but no consensus yet.

  4. Candidates of Dibaryons Candidates of Multi-Strangeness Dibaryons. • Chiral soliton quark model prediction of theΘ+ played a vital role in the “discovery” of Θ+. Quark model predictions of dibaryon: 1. H(uuddss) I=0,Jp=0+,S=-2 Wang Zhang others Threshold M(MeV) 2228 2223 deeply bound 2231 2230 2233 to unbound (2230-32) Quite impossible to be deeply bound. More than 25 years search with null result.

  5. 2.  I=0,Jp=0+,S=-6 Wang Zhang Others Threshold M(MeV) 3298 3229 deeply bound 3345 3300 3292 to unbound (3300-4) Similar to H particle, weakly bound or unbound.

  6. 3.N I=1/2,Jp=2+,S=-2 Wang Zhang Others Threshold M(MeV) 2549 2561 deeply bound 2611 2557 2607 to unbound (2590) (keV) 12-22 Decay mode N--> 1D2,3D2. Quite possible a narrow resonance. (Wang:PRL 59(87)627, 69(92)2901, PRC 51(95)3411, 62(00)054007, 65(02)044003, 69(04)065207; Zhang:PRC 52(95)3393, 61(00)065204, NPA 683(01)487.)

  7. RHIC, a multiquak factory RHIC is a factory of multiquark states especially multi strangeness dibaryons. High strangeness production. Hadronization and clustering at the boundary of fire ball. Shandong group estimation: no problem to produce N in one event, but hard to have  in one event.

  8. Nonperturbative QCD basis of quark models Nonperturbative QCD basis of quark models. How reliable are these quark model predictions? Wang(QDCSM or Nanjing-Los Alamos model) Zhang(chiral quark model or Tokyo-Tuebingen-Beijing -Salamanka model) both fit the existed NB scattering data(Zhang’s better) and deuteron properties(Wang’s better). The effective attraction developed in  and N channels is quite model independent. There are many other quark models but I will not talk about them here.

  9. Quark-Goldstone boson coupling From current-quark gluon QCD to constituent quark Goldstone boson effective theory ‘t Hooft-Shuryak-Diakonov dilute instanton liquid vacuum(DILM). (NPB 203,245,461) Negele’s lattice QCD supports DILM(fig.1).(PRD 49(94)6039) Our group reproduced part of Negele’s result. It has not been proved but might be a good approximation of QCD vacuum.

  10. Current quark propagating within the DILM(fig.2) (NPB 272(86)457; hep-ph/0406043) Current quark m is dressed to be constituent quark M(q2) (fig.3) The QCD Lagrangian is transformed to be the effective Lagrangian

  11. Our group derive an effective Lagrangian based on chiral symmetry spontaneously broken and its nonlinear realization, The constituent quark field operatorc is related to the current quark operator by

  12. The form of dynamically derived effective Lagrangian, such as the former Diakonov’s Lagragian, is model dependent, but the nonlinear coupling is dictated by the chiral symmetry spontaneously broken as we did. The linear approximation of Zhang(NPA 683(01)487)and others, such as Glozman & Riska, Phys. Reports, 268(96)263, missed the higher order terms, which should be important for short range physics, such as multi quark study. The SU(3) extension of linear approximation is even questionable, the universal u,d,s-σquark meson coupling will over estimate the σinduced attraction with strangeness particles.

  13. QDCSM Nanjing-Los Alamos model • QCD basis of Nanjing-Los Alamos model The constituent quark-Goldstone boson coupling effective Lagrangian is still a nonperturbative strong interaction field theory. We did a self consistent mean field approximation calculation and found that the self-consistent meson mean field increases as the increasing of quark excitation, i.e., the mean field try to keep the quark confined, within a limited excitation.

  14. Quenched lattice QCD calculation(hep-lat/0407001 and the ref.’s there in)) shows that the ground state gluon field energy for systems can all be expressed as where the Lmin is the minimum length of the gluon flux tube or string.(fig.4)(hep-lat/0407 Unquench will modify the long range behavior by color screening(fig.5).

  15. For individual color configuration, the quenched lattice QCD result can be approximately expressed by a two body confinement potential,(Nuovo Cmento, 86A(85)283) Vij=-kλiλjrijp p=1,2, the unquenched one can be approximated as Vij=-kλiλj rijp (1-exp(-μrijp))/μ, p=1,2, μis color screening constant. These color configurations will be mixed due to gluon fluctuation and excitation.

  16. In the naïve quark model, meson and baryon have unique color structure: baryon meson So De Rujula, Georgi, Glashow and Isgur can have simple Hamiltonian for hadron spectroscopy.

  17. For pentaquark there are more color structures: ……

  18. In principle one should have a multi body interaction, multi channel coupling model. Numerically it is quite Involved. We developed a quark delocalization, color screening model (QDCSM), where the multi color couplings are modeled by an extended effective matrix elements within a two cluster Hilbert space where the color screening constant μis left as a variational parameter; the multi quark orbital configurations are modeled by means of delocalized quark orbits within a two cluster space where the delocalization parameterεis left as another variational parameter.

  19. The variational calculation will allow the multi quark system to adjust themselves to arrive at a • self consistency. • We can not derive this model from QCD. The fit of hadron interaction data shows that this model comprises right physics at least partly.

  20. Proposal • H particle : At most weakly bound or unbound, keep it as a candidate at RHIC search , but not very promised. • Di- Possibly a weakly bound state, keep it as another candidate, but the production rate is very low. • N The most promised one, it is a very narrow resonance around 2.55 GeV, even narrower than the Θ+.

  21. Thanks 谢谢(xie xie)

  22. QDCSM • Hamiltonian:

  23. RGM

  24. Wavefunctions:

  25. Model Parameters • M=313 MeV, b=0.602 fm, αs=1.555, a=25.03 MeV/fm2, Ms=634 MeV. r0=0.8 fm are fixed by ground state masses of baryons • μ=0.9 fm-2 Is fixed by deuteron properties, should be adjusted for every multi quark system. • Delocalization parameterεis determined for every separation and every channel by the dynamics of the multi quark system

  26. Dibaryons • Deuteron(Strangeness=0,I=0,J=1) : Md=1875.8 MeV, =1.92 fm, PD=4.92%, two-baryon state TheΔΔ components of deuteron is consistent with the Salamanca result. • H(Strangeness=-2,I=0,J=0): First predicted by Jaffe in 1977 with MIT bag model. MH=2228-2230 MeV. A weakly bound or unbound one.

  27. d* (Strangeness=0,I=0,J=3): Md*=2165 MeV, =1.3 fm. (6-quark state) Γ(d*NN D-wave)=7 MeV. Quite different from Zhang’s ,because of the different Mechanisms of intermediate range attraction. • di-Ω(Strangeness=-6,I=0,J=0): M Ω Ω=3300 MeV, =1.2 fm. (6-quark state) Quite different from Zhang’s, because of the different mechanisms of intermediate range attraction. • d’ (Strangeness=0,I=0,J=0,Parity=-): 2060 MeV Md’=2454 MeV. Original resonance signal disappeared later.

  28. ΔΔ(I=0,J=1): MΔΔ=2078 MeV, Γ(ΔΔNN S-wave)=147 MeV • ΔΔ(I=1,J=0): MΔΔ=2131 MeV, Γ(ΔΔNN S-wave)=228 MeV • ΔΔ(I=1,J=2): MΔΔ=2205 MeV, Γ(ΔΔNΔ S-wave)=10 MeV

  29. NΩ(I=1/2,J=2): MΔΔ=2549 MeV, Γ (NΩΛΞ S=0, D-wave )=0.012 MeV Γ (NΩΛΞ S=1, D-wave )=0.022 MeV Pysical reasons for narrow width: D-wave dicay, tensor interaction, no π in N channel, One quark must be exchanged between N and . Quite possible a narrow resonance.

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