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Heavy Quarkonia in a Hot Medium

Heavy Quark Workshop, BNL December 12-14, 2005. Heavy Quarkonia in a Hot Medium. Introduction The potential between Q and Q extracted from lattice gauge calculations Stability of heavy quarkonia in a hot medium ◘ above Tc ◘ below Tc Quark drip lines in quark-gluon plasma Conclusions

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Heavy Quarkonia in a Hot Medium

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  1. Heavy Quark Workshop, BNL December 12-14, 2005 Heavy Quarkonia in a Hot Medium • Introduction • The potential between Q and Q extracted from lattice gauge calculations • Stability of heavy quarkonia in a hot medium • ◘ above Tc • ◘ below Tc • Quark drip lines in quark-gluon plasma • Conclusions • C.Y.Wong,PRC65,034902(’02);PRC72,034906 (’05) • C.Y.Wong, hep-ph/0509088 Cheuk-Yin Wong Oak Ridge National Laboratory & University of Tennessee

  2. Introduction • Successes of the phenomenological recombination model suggest the possibility that heavy and light quarkonia may be bound in quark-gluon plasma • Two new surprising results from lattice gauge calculations • Lattice spectral function analyses in quenched QCD show that J/ψ is stable up to 1.6Tc • Lattice static Q-Q “potential” appears to be very strong between 1 and 2 Tc • Shuryak, Zahed, Brown, Lee, and Rho suggested that even light quarkonia may be bound in quark-gluon plasma

  3. We need • to confirm these lattice gauge results • to study effects of dynamical quarks on J/ψ stability • to assess the strength of the Q-Q potential • to examine the stability of heavy and light quarkonia in quark-gluon plasma to provide useful support to the recombination model and the thermal model of chemical yields

  4. Lattice gauge spectral analyses in the quenched approximation show that the width of J/ψ remains narrow up to T ≤ 1.6 TC 403x40 483x24 322x48x128 M. Asakawa, T. Hatsuda, and Y. Nakahara, Nucl. Phys. A715, 863 (03) S. Datta, F. Karsch, P. Petreczky, and I. Wetzorke, Phys. Rev. D69,094507(04) The drastic change of the spectral function between 1.62-1.70Tc suggests the occurrence of spontaneous dissociation at 1.62-1.70Tc.

  5. Questions: • What does the potential model say about the J/ψ spontaneous dissociation temperature? • What are the effects of dynamical quarks on the spontaneous dissociation temperature? 3 What is the strength of interaction between a static quark and antiquark? Can it be so strong as to bind light quark-antiquark pairs?

  6. Kaczmarek et al. calculated the color-singlet F1 and U1 in the quenched approximation [hep-lat/0309121] F1(r,T) was calculated in the Coulomb gauge U1 is much deeper and broader than F1 and can hold many more bound states

  7. What is the Q-Q potential? 1. The free energy F1(r,T) as the Q-Q potential (Digal et.al `01,Wong `02) 2. The internal energy U1(r,T)=F1(r,T)+TS1(r,T) as the Q-Q potential (Kaczmarek et al.`02,Shuryak et al `04)

  8. How to get the Schrödinger equation for a Q-Qbar pair? • Consider a static color-singlet Q and Qbar separated by a distance r in a gluon medium at temperature T in quenched QCD. Get F1, U1, andTS1= U1 - F1

  9. 2. Study a dynamical Q-Qbar in motion in the gluon medium. For a fixed temperature and volume, the equilibrium of the Q-Qbar and gluons is reached when the grand potential A is a minimum.

  10. How to subtract Ug from U1?

  11. Quenched QCD equation of state F1 and U1 fractions depend on T Boyd et al. (Nucl. Phys. B ’96) F1 fraction U1 fraction

  12. Solve for Q-Q bound states (1)

  13. Q-Q potential at T<Tc for QCD (2 flavors) Karsch, Laemann, and Peikert, NPB605,579(`01) Full QCD(2 flavor) Q-Qbar potential is taken to be the free energy in lattice gauge calculations. C.Y.Wong, PRC65,034902 (`02)

  14. T<Tc T>Tc (1) Full QCD (2 flavors) Quenched QCD C.Y.Wong, PRC65,034906 (`05) C.Y.Wong, PRC65,034902 (`02)

  15. T<Tc T>Tc Quenched QCD Full QCD (2 flavors)

  16. Spontaneous dissociation temperatures in quenched QCD

  17. Quenched QCD & Full QCD • Quenched QCD is inadequate as it neglects the effects of dynamical quarks • We need to study full QCD with dynamical quarks • Kaczmarek et al. (PRD 71, 114510 ΄05) have obtained F1 and U1 in full QCD (with 2 flavors) • Karsch et al. (PLB 478, 447) obtained the equation of state in full QCD (with 2 flavors) from which we get a(T)=3p/ε. • We can use the potential model to study the stability of quarkonium in full QCD

  18. Full QCD with two flavors Kaczmarek et al (’05)

  19. Full QCD with two flavors

  20. Spontaneous dissociation temperatures in quenched QCD & full QCD

  21. Recent lattice calculations in 2-flavor QCD J/ψ spectral function (~Tc) (~2Tc) Aarts et al., hep-lat/0511028 J/ψ appears to have narrow width even up to ~2Tc in full QCD

  22. Quarkonia in quark-gluon plasma The Q-Qbar potential extracted from lattice calculations can be used to examine the stability of light and heavy quarkonia. We can treat the quark mass as a variable and obtain the spontaneous dissociation temperature as a function of the reduced mass.

  23. The quark drip line • The quark drip line is the line in the (μ,T) space above which a Q-Qbar is unbound. • It can be characterized by the nature of the Q-Qbar state: 1s drip line, 1p drip line,.. • Given the Q-Qbar potential, the drip line can be determined by locating the spontaneous dissociation temperature as a function of the reduced mass.

  24. Quark drip lines in quark-gluon plasma in quenched QCD

  25. Stability of quarkonia in quark-gluon plasma in full QCD Dynamical quarks modifies the 1s drip line but only slightly the 1p drip line. potential

  26. Use quark drip lines to study light quarkonia • Because of the strong coupling, light quarks become quasiparticles and acquire masses • The quasiparticle masses of quarks in quark-gluon plasma can be estimated by looking at the equation of state (Levai et al. `98, Szabo et al.`02, Iavanov et al.`05). They found that the quasi-particle masses of u, d, and s quarks are mq~ 0.3-0.4 GeV for Tc<T<2Tc.

  27. Light quark quarkonia For light quarks with a mass of 300-400 MeV, the quark drip lines show that quarkonia with light quarks can be stable up to 1.06Tc. Szabo et al. JHEP 0306, 008 (`03) Results from Levai et al `98 and Ivanov et al `05 are similar.

  28. Quark quasiparticle mass from lattice gauge calculations Lattice gauge theory calculations give the quasiparticle mass of light quark (Petreczky et al. `02) With such a heavy quark mass, quarkonia with (u,d,s) quarks can be bound up to 1.31 Tc. In either case, the region of possible quarkonia with light quarks is limited to temperatures close to Tc.

  29. Conclusions • The potential model is consistent with the lattice gauge spectral function analysis, if the Q-Qbar potential is a linear combination of F1 and U1,with coefficients that depend on the equation of state. • The effects of the dynamical quarks modify only slightly the stability of J/ψ. J/ψ dissociates spontaneously at about 1.62 Tc in quenched QCD and at 1.42 Tc in 2-flavor QCD. • The interaction between a static quark and antiquark is such that the quark drip lines limit possible quarkonium states with light quarks to temperatures close to Tc.

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