Properties of Quarkonia at Tc Su Houng Lee

Properties of Quarkonia at Tc Su Houng Lee In collaboration with Kenji Morita 1

J/y in Quark Gluon Plasma 1986: Hashimoto, 1986: Matsui, Miyamura , . . : Mass shift of J/ Satz : J/ y will dissolve at y Near Tc Tc T< 1. 6 Tc 1988: Hansson , Lee, Zahed : J/ y states in QGP 2004: Asakawa , Hatsuda : J/ y will survive up to 2 Confirmed by other lattice calculations: Datta etal. Tc T> 1. 6 Tc and potential model: Wong. . . S H Lee 2

J/y in Quark Gluon Plasma • Tc <T<2 Tc is important in HIC Kolb, Heinz, nucl-th/0305084 • Large uncertainty in lattice MEM Jakovac et al. hep-lat/0611017 • Tc <T<2 Tc is non perturbative region T=0 phenomenological approach? S H Lee J/y High T perturbative approach? Karsch hep-lat/0106019 3

How can we treat heavy quark system in QCD ? Properties of QGP from lattice S H Lee 4

G 2, E 2 and B 2 across Tc -- (quenched case) Using energy momentum tensor p and e local operators e/T 4 p/T 4 Lattice result for purge gauge (Boyd et al 96) <a/p B 2 >T =0 D<a/p G 2 >T <a/p E 2 >T Maximum at 1. 1 Tc Extraction from lattice: Morita, Lee (08) S H Lee 5

E 2 and B 2 across Tc -- (relation to potentials ? ) Manousakis, Polonyi, PRL 58 (87) 847 “Nonperturbative length scale in high T QCD” Shifman NPB 73 (80) Time W(S-T) = 1 - <a/p E 2> (ST)2 +… W(S-T) W(S-S) = 1 - <a/p B 2> (SS)2 +… a. Exp(-b. F) L Space L W(S-S) Space W(S-T) T< Tc Area T> Tc Perimete r <a/ p. E 2 > W(S-S) change Area <a/ p. B 2 > no change Area If <E 2> suddently increases across Tc, what will happen to J/y immersed in it ? S H Lee 6

Hydrogen Atom in an external E field <E >external S H Lee <E 2 >T 7

QCD 2 nd order Stark Effect (Peskin , Luke, Manohar ) D<a/p E 2 >T Attractive for ground state T/ Tc 1. 05 e 0 Dm J/ y -44 Me. V -105 Me. V 311 Me. V Dm U -4. 3 Me. V -10 Me. V 580 Me. V A non-perturbative method ? S H Lee 8

Basics in Heavy quark system Heavy quark propagation Perturbative treatment are possible because S H Lee 9

System with two heavy quarks Perturbative treatment are possible when S H Lee 10

Perturbative treatment are possible when S H Lee q 2 process 0 Photo production of open charm expansion parameter example m 2 J/ y > 0 Bound state properties Formalism by Peskin (79) J/y dissociation: NLO J/y mass shift: LO -Q 2 < 0 QCD sum rules for heavy quarks Predicted mhc <m. J/y before experiment 11

Including Temperature effects For High T > 2 Tc Separation scale For small and close to Tc S H Lee T 12

A reliable non perturbative approach near T c at q 2 < 0 Morita, Lee: ar. Xiv: 0704. 2021 (PRL 08) ar. Xiv: 0711. 3998 S H Lee 13

QCD sum rules for Heavy quark system T=0 Phenomenological side OPE r J/y Y’ s predicted Mhc<MJ/y before experiment S H Lee 14

QCD sum rules for Heavy quark system T near Tc Phenomenological side OPE r J/y D<G 2>+c<G 2> Y’ s D<G 2> Matching M OPE n-1 /M n from Phen Obtain constraint for to Dm J/ y and G For Detail Kenji Morita’s Poster S H Lee 15

Constraint for J/y Mass and Width above Tc If G=0 e/T 4 p/T 4 Dm Ge. V If Dm=0 G Me. V |Dm|+G =15 x. T, near Tc S H Lee 16

Summary Due to the sudden change in gluon condensates, there will be a critical behavior of J/y near Tc, |Dm|+ DG =150 Me. V from Tc to Tc + 10 Me. V • Model calculation is needed to get the changes separately, Use QCD Stark Effect ? From G =constraint- Dm (Stark effect) G QCD sum rule constraint with DG=0 S H Lee 17

Summary 1. ‘Order parameter’ of QCD Phase transition: Critical behavior of J/y near Tc, mass shift and width broadening from QCD sum rules, |Dm|+ DG =200 Me. V from 0. 98 T c to 1. 05 T c with Stark effect: Dm=-100 Me. V , G=100 Me. V at 1. 05 T c 2. A precursor phenomena takes place in nuclear matter Mass shift could be observed through anti proton project at GSI 3. Consequences in HIC? . Non trivial effects expected to cc , y’, U, U’… 4. S H Lee Remember the many findings from Stark, Zeeman, Anomalous Zeeman effects… Challenges for future experiments and analysis ! 18