1. Heavy Quarkonia in a Hot Medium Cheuk-Yin Wong Oak Ridge National Laboratory & University of Tennessee Heavy Quark Workshop, BNL December 12-14, 2005 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

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 T C 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. 32 2 x48x128 40 3 x40 48 3 x24

5. Questions: 1What does the potential model say about the J/ψ spontaneous dissociation temperature? 2What 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 F 1 and U 1 in the quenched approximation [hep-lat/0309121] F 1 (r,T) was calculated in the Coulomb gauge U 1 is much deeper and broader than F 1 and can hold many more bound states

7. What is the Q-Q potential? 1. The free energy F 1 (r,T) as the Q-Q potential (Digal et.al `01,Wong `02) 2. The internal energy U 1 (r,T)=F 1 (r,T)+TS 1 (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? 1.Consider a static color-singlet Q and Qbar separated by a distance r in a gluon medium at temperature T in quenched QCD. Get F 1, U 1, and TS 1 = U 1 - F 1

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.

11. How to subtract U g from U 1 ?

12. F 1 and U 1 fractions depend on T Boyd et al. (Nucl. Phys. B ’96) Quenched QCD equation of state F1 fraction U1 fraction

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

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

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

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

17. Spontaneous dissociation temperatures in quenched QCD Heavy Quarkonium Spectral Analysis Potential F 1 Potential U 1 Potential J/ψ 1.62-1.70T C 1.62T C 1.40T C 2.60T C χ c, ψ ' below 1.1 T C unbound 1.18T C Υ 4.10T C 3.50 T C ~ 5.0 T C χ b 1.15-1.54 T C 1.19T C 1.10T C 1.73T C

19. 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 F 1 and U 1 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

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

21. Full QCD with two flavors

22. Spontaneous dissociation temperatures in quenched QCD & full QCD Heavy Quarkonium Quenched QCD 2-flavor QCD Spectral Analysis Quenched QCD J/ψ 1.62T C 1.42T C ~ 1.6 T C χ c, ψ ' unbound below 1.1 T C Υ 4.10T C 3.30 T C χ b 1.18T C 1.22T C 1.15-1.54

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

24. 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.

25. 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.

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

27. 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

28. 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 m q ~ 0.3-0.4 GeV for Tc<T<2Tc.

29. Light quark quarkonia Szabo et al. JHEP 0306, 008 (`03) Results from Levai et al `98 and Ivanov et al `05 are similar. 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.

30. 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.

31. The potential model is consistent with the lattice gauge spectral function analysis, if the Q-Qbar potential is a linear combination of F 1 and U 1,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. Conclusions