1 Meson mass in nuclear medium Su Houng Lee Thanks to: Hatsuda + former collaborators + and to Kenji Morita(GSI) and Taesoo Song(A&M) 1.Phase transition, order parameter and nuclear matter 2.Light quark system (Few comments on theory and recent experiments) 3.Heavy quark system (Few comments on recent theory and outlook) S H Lee: 1/8/10 KEK 2 Phase transition, order parameter and nuclear matter S H Lee: 1/8/10 KEK 3 Confinement: L=e -F Chiral sym: EOS: e, p Heavy quark V(r) Lattice results for phase transition in QCD (from Karschs review) Susceptibility mq L Quark number q S H Lee: 1/8/10 KEK 4 At finite temperature: from Local operator related to confinement? Gluon Operators near Tc Two independent operators Twist-2 Gluon Gluon condensate or T G0G0 G2G2 S H Lee: 1/8/10 KEK 5 W(ST)= exp(- ST) Time Space S W(S-T) = 1- (ST) 2 + W(S-S) = 1- (SS) 2 + OPE for Wilson lines: Shifman NPB73 (80), vs confinement potential Local vs non local behavior W(SS)= exp(- SS) T Behavior at T>Tc W(SS)= exp(- SS) W(ST)= exp(- g(1/S) S) T S H Lee: 1/8/10 KEK 6 Linear density approximation Condensate at finite density At = 5 x n.m. Local operators in Nuclear Medium S H Lee: 1/8/10 KEK 7 QCD vacuum Nuclear medium : partially deconfined and chiral symmetry restored S H Lee: 1/8/10 KEK 8 Light quark system Many review: Hayano, Hatsuda, arXiv: Here, 1.Few comments on momentum dependence 2.Few comments on two recent experiments S H Lee: 1/8/10 KEK 9 Order parameters Hadronic world Hadronic world : Spontaneously broken chiral symmetry D(1870) 0- D(2400)? 0+ D*(2007) 1- D1(2420) 1+ Ds(1968) Ds(2317) D*(2112) Ds1(2460) 530 ? S H Lee: 1/8/10 KEK 10 Few comments on vector meson mass shift from QCD sum rules Vacuum saturation hypothesis ( Hatsuda & Lee92 ) For meson For A 1 meson For meson Can such signal survive trivial smearing effects ? S H Lee: 1/8/10 KEK 11 T, L components in vector meson Momentum dependence To be safe, |q| 0.8 GeV S H Lee: 1/8/10 KEK 14 Heavy quark system 1.Comments on heavy quark system near Tc 2.In nuclear matter S H Lee: 1/8/10 KEK 15 Tc region is important in HIC Few things to note about J/ near Tc Large non-perturbative change at Tc Resumed perturbation fails Karsch hep-lat/ T (GeV) Au+Au 200 Agev, b=0 (fm/c) (e-3p)/T 4 T/T c S H Lee: 1/8/10 KEK 16 Approach based on OPE In this work, Separation of scale in this approach Non perturbative perturbative 1.J/ mass shift (m) near Tc: QCD 2 nd order Stark effect 2.J/ width () near Tc : perturbative QCD + lattice 3.check consistency of m, at Tc :QCD sum rules 4.Application to nuclear matter T S H Lee: 1/8/10 KEK 17 OPE for bound state: m infinity Mass shift: QCD 2 nd order Stark Effect : Peskin 79 > qcd Attractive for ground state S H Lee: 1/8/10 KEK 18 2 nd order Stark effect from pNRQCD LO Singlet potential from pNRQCD : Brambilla et al. Derivation 1/r > Binding > QCD, Take expectation value Large Nc limit Static condensate Energy S H Lee: 1/8/10 KEK 19 Summary Elementary J/ in pert QCD, LO (Peskin + others) and NLO (Song, Lee 05) LO NLO Thermal width from NLO QCD + confinement model Thermal width: J/ x thermal gluon (Park, Song, Lee, Wong 08,09) S H Lee: 1/8/10 KEK 20 E,B Condensate Confinement model: Schneider, Weise S H Lee: 1/8/10 KEK 21 Summary =pert QCD + confinement model GeV / J M m from QCD Stark Effect Mass and width of J/ near Tc (Morita, Lee 08, M, L & Song 09) S H Lee: 1/8/10 KEK 22 Constraints from QCD sum rules for Heavy quark system OPE Phenomenological side s J/ sum rule at T=0 : can take any Q 2 >=0, S H Lee: 1/8/10 KEK 23 QCD sum rule constraint (Morita, Lee 08) MeV] m MeV] Can also use Borel sum rule S H Lee: 1/8/10 KEK 24 Summary =pert QCD + confinement model GeV / J M m from QCD Stark Effect Mass and width of J/ near Tc (Morita, Lee 08, M, L & Song 09) QCD sum rule limit with =0 =constraint-m (Stark effect) S H Lee: 1/8/10 KEK 25 Summary in NLO QCD + confinement model Non perturbative part at Tc: confinement model (m g (T) C(T)) From Tc to 1.05 Tc mass and width seems to rapidly change by 50 MeV ; to probe higher temperature within this region, 1.For mass, need higher dimensional operators 2.For width, Need higher twist contribution Constraints from Borel sum rule NLO QCD + confine-model S H Lee: 1/8/10 KEK 26 Two places to look Reconstruction of Imaginary Correlator and R AA from RHIC S H Lee: 1/8/10 KEK 27 Reconstruction of Imaginary correlator J/ Imaginary correlator w mS0S0 Reconstructed correlator S H Lee: 1/8/10 KEK 28 Morita, Lee (09) arXiv: S H Lee: 1/8/10 KEK 29 2-comp model (Rapp) Comparison with experimental data of RHIC (s=200 GeV at midrapidity) T. Song, SHLee (preliminary) Melting of c Slope: J/ Melting T of J/ Height: mass of J/ S H Lee: 1/8/10 KEK 30 Effects of width and mass At LHC Mass shift by -100 MeV Assumed recombination effect to be the same S H Lee: 1/8/10 KEK 31 Quantum numbers QCD 2 nd Stark eff. Potential model QCD sum rules Effects of DD loop c 0 -+ 8 MeV5 MeV (Klingl, SHL,Weise, Morita) No effect J/ 1 -- 8 MeV (Peskin, Luke) -10 MeV (Brodsky et al). 7 MeV (Klingl, SHL,Weise, Morita)