Stability of Quarkonia in a Hot Medium Cheuk-Yin Wong Oak Ridge National Laboratory & University of Tennessee SQM Workshop, UCLA, March 26-30, 2006 Introduction How to extract the Q-Q potential from LGT results Quarkonium bound states in a hot medium Quark drip lines in quark-gluon plasma Conclusions C.Y.Wong,PRC65,034902(’02);PRC72, (’05) C.Y.Wong, hep-ph/

2 Why study quarkonia in a hot medium?  Successes of the recombination model suggest 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 indicate that J/ψ may be stable up to 1.6Tc Lattice static Q-Q “potential” appears to be very strong between 1 and 2 Tc

3  We need to confirm these lattice gauge results to examine the stability of quarkonia to study effects of dynamical quarks on quarkonium stability

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 suggests the occurrence of spontaneous dissociation between 1.62 and 1.70Tc x48x x x24

5 Kaczmarek et al. calculated the color-singlet F 1 and U 1 in the quenched approximation [hep-lat/ ] F 1 (r,T) was calculated in the Coulomb gauge Rσ 1/2

6 U 1 is much deeper and broader than F 1 and can hold many more bound states O. Kaczmarek et al. hep-lat/ U1U1 F1F1 Using U 1 as the potential,, Shuryak, Zahed, Brown, Lee, and Rho suggested that even light quarkonia may be bound in quark-gluon plasma T/T c =1.3 R

7 What is the Q-Q potential? As ansatzes: 1. F 1 (r,T), the free energy (Digal et.al `01, Wong `02, Blaschke `05) 2. U 1 (r,T)=F 1 (r,T)+TS 1 (r,T), the internal energy (Kaczmarek et al.`02, Shuryak et al `04, Alberico `05) With theoretical justifications : 3. A linear combination of F 1 and U 1 (Wong,PRC 72,034906`05)

8 We need to understand the meaning of U 1. We need to understand the meaning of TS 1 =U 1 -F 1. T/T c =1.3 Why such behavior? R (fm) O. Kaczmarek et al. hep-lat/

9 Implications of S 1 (R) increases as R increases

10 Simple model of charge screening Q (charge +q) at -R/2 Q (charge –q) at R/2 medium: e + (charge +q), e - (charge –q) particles interact with an e 1 e 2 /r interaction We assume e + and e - are massless and are fermions. We also assume local thermal equilibrium

11

12

13,

14 Total entropy, particle number, and increases and saturates as R increases. R

15 Total medium entropy, particle number, and internal energy increase (and saturate) as R increases. R

16

17 C.Y.Wong,PRC72, (’05)

18 How to separate out U g from U 1 ?

19 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

20 Solve for Q-Q bound states (1)

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

22 Spontaneous dissociation temperatures in quenched QCD Heavy Quarkonium Spectral Analysis Potential F 1 Potential U 1 Potential J/ψ T 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 T C 1.19T C 1.10T C 1.73T C

23 Quenched QCD & Full QCD Quenched QCD is inadequate as it neglects the effects of dynamical quarks Dynamical quarks provide additional screening F 1 and U 1 for full QCD (with 2 flavors) have been obtained by Kaczmarek et al. ΄05 The equation of state for full QCD (with 2 flavors) has been obtained by Karsch et al. ΄02.

24 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

25 Quarkonia in quark-gluon plasma We can treat the quark mass as a variable and obtain the binding energies of a quarkonium as a function of the reduced mass μ red and temperature T. Stability represented by ‘quark drip lines’ In the ( T, quark reduced mass μ red ) space, the quark drip line is the line below which a quarkonium is unbound. There are 1s drip line, and 1p drip line, etc,…

26 Quark drip lines in quark-gluon plasma Unbound Region

27 Use quark drip lines to determine the stability of light quarkonia Because of the strong interaction, light quarks become quasiparticles and they acquire masses These masses can be estimated by studying 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 ~ GeV for Tc<T<2Tc.

28 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 MeV, the quark drip line shows that quarkonia with light quarks can be stable up to 1.06Tc.

29 The potential model is consistent with the spectral function analysis, if the Q-Q 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 J/ψ stability only slightly. In quenched QCD,. J/ψ dissociates spontaneously at 1.62 T c. In full QCD with 2 flavors, J/ψ dissociates spontaneously at 1.42 T c Light quarkonium states may be stable up to ~1.06 T c. The stability of these light quarkonia near T c provides support to the recombination model at temperatures just above T c. Conclusions

30