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 Karsch’s 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|<0.5 GeV Or Separate measurement of L, T component n.m. 3x n.m. q TL Importance of momentum dependence (Lee98)

S H Lee: 1/8/10 KEK 12 Width with constant cross section Width for momentum dependent cross section Example: momentum dependent Medium width  k  nn

S H Lee: 1/8/10 KEK 13 Few comments on Experiments outside Japan CBELSA/TAPS PRL 94 (05) :  mass reduction 16% CBELSA/TAPS Recent reanalysis: background generated from   4  events, omitting 1   more subtraction blow 700 MeV CLAS: no mass shift observed, but 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 MeV–5 MeV (Klingl, SHL,Weise, Morita) No effect J/  1 -- –8 MeV (Peskin, Luke) -10 MeV (Brodsky et al). –7 MeV (Klingl, SHL,Weise, Morita) <2 MeV (SHL, Ko) c c 0,1, MeV-15 MeV (Morita, Lee) No effect on  c1  (3686) MeV< 30 MeV  (3770) MeV< 30 MeV Applications for mass shift in nuclear matter

S H Lee: 1/8/10 KEK 32 Anti proton Heavy nuclei Observation of  m through p-A reaction at PANDA Expected luminosity at GSI 2x cm -2 s -1 Can be done at J-PARC

S H Lee: 1/8/10 KEK 33 1.Nuclear matter: non trivial change characteristic of QCD phase transition 2.To see Vector meson mass shifts, they have to be produced almost at rest to avoid trivial smearing effect 3 Nuclear matter also cause J/ ,  c to change mass of 7, 15 MeV.  Larger effect for  (3686),  (3770) Summary 4. Such effects could be searched at FAIR, J-PARC