Meson mass in nuclear medium

1. Meson mass in nuclear medium Su Houng Lee Thanks to: Hatsuda + former collaborators + and to Kenji Morita(GSI) and Taesoo Song(A&M) Phase transition, order parameter and nuclear matter Light quark system (Few comments on theory and recent experiments) Heavy quark system (Few comments on recent theory and outlook)

2. Phase transition, order parameter and nuclear matter

3. EOS: e , p Quark number cq Lattice results for phase transition in QCD (from Karsch’s review) Heavy quark V(r) Confinement: L=e-F Chiral sym: <qq> Susceptibility cmqcL

4. G0 <a/p B2>T <a/p E2>T G2 Local operator related to confinement? Gluon Operators near Tc • Two independent operators Gluon condensate or Twist-2 Gluon • At finite temperature: from

5. <E2>, <B2> vs confinement potential • Local vs non local behavior Time W(ST)= exp(-s ST) OPE for Wilson lines: Shifman NPB73 (80) T S W(S-T) = 1- <a/p E2> (ST)2 +… W(S-S) = 1- <a/p B2> (SS)2+… Space W(SS)= exp(-s SS) Space • Behavior at T>Tc W(SS)= exp(-s SS) <a/p B2>T W(ST)= exp(-g(1/S) S) <a/p E2>T

6. Local operators in Nuclear Medium • Linear density approximation • Condensate at finite density • At r = 5 xrn.m.

7. Nuclear medium : partially deconfined and chiral symmetry restored QCD vacuum

8. Light quark system • Many review: Hayano, Hatsuda, arXiv:0812.1702 • Here, • Few comments on momentum dependence • Few comments on two recent experiments

9. Hadronic world : Spontaneously broken chiral symmetry • Order parameters • Hadronic world Ds1(2460) D1(2420) D(2400)? Ds(2317) 348 413 349 530 ? D*(2112) D*(2007) Ds(1968) D(1870) 144 137 0- 0+ 1- 1+ 0- 0+ 1- 1+

10. Few comments on vector meson mass shift from QCD sum rules • Vacuum saturation hypothesis ( Hatsuda & Lee92 ) For r meson For A1 meson For j meson Can such signal survive trivial smearing effects ?

11. Importance of momentum dependence (Lee98) L T • T, L components in vector meson q • Momentum dependence n.m. To be safe, |q|<0.5 GeV Or Separate measurement of L, T component 3x n.m.

12. Example: momentum dependent Medium width • Width with constant cross section w, k b n • Width for momentum dependent cross section

13. Few comments on Experiments outside Japan • CBELSA/TAPS PRL 94 (05) : w mass reduction 16% CBELSA/TAPS Recent reanalysis: background generated from pp, ph 4 g events, omitting 1 g  more subtraction blow 700 MeV • CLAS: no mass shift observed, but qr > 0.8 GeV

14. Heavy quark system • Comments on heavy quark system near Tc • In nuclear matter

15. Few things to note about J/y near Tc • Tc region is important in HIC Au+Au 200 Agev, b=0 T (GeV) t (fm/c) • Large non-perturbative change at Tc (e-3p)/T4 T/Tc • Resumed perturbation fails Karsch hep-lat/0106019

16. <a/p B2>T <a/p E2>T Approach based on OPE • Separation of scale in this approach Non perturbative perturbative • In this work, • J/y mass shift (Dm) near Tc: QCD 2nd order Stark effect • J/y width (G) near Tc : perturbative QCD + lattice • check consistency of Dm , G at Tc :QCD sum rules • Application to nuclear matter

17. = Mass shift: QCD 2nd order Stark Effect : Peskin 79 e > Lqcd • OPE for bound state: m infinity • Attractive for ground state

18. 2nd order Stark effect from pNRQCD • LO Singlet potential from pNRQCD : Brambilla et al. 1/r > Binding > LQCD, • Derivation • Take expectation value • Large Nc limit • Static condensate • Energy • 

19. Thermal width from NLO QCD + confinement model Summary • Elementary sJ/y in pert QCD, LO (Peskin + others) and NLO (Song, Lee 05) LO NLO • Thermal width: sJ/y x thermal gluon (Park, Song, Lee, Wong 08,09)

20. Confinement model: Schneider, Weise • E,B Condensate

21. D M y / J GeV Mass and width of J/y near Tc (Morita, Lee 08, M, L & Song 09) Summary Dm from QCD Stark Effect G =pert QCD + confinement model

22. Constraints from QCD sum rules for Heavy quark system • sum rule at T=0 : can take any Q2 >=0, Phenomenological side OPE r J/y Y’ s

23. QCD sum rule constraint (Morita, Lee 08) G [MeV] G [MeV] Dm [MeV] Dm [MeV] Can also use Borel sum rule

24. D M y / J GeV G Mass and width of J/y near Tc (Morita, Lee 08, M, L & Song 09) Summary Dm from QCD Stark Effect QCD sum rule limit with DG =0 G =constraint-Dm (Stark effect) G =pert QCD + confinement model

25. NLO QCD + confine-model G in NLO QCD + confinement model Summary • Non perturbative part at Tc: confinement model (mg(T) C(T)) Constraints from Borel sum rule • From Tc to 1.05 Tc mass and width seems to rapidly change by 50 MeV ; to probe higher temperature within this region, • For mass, need higher dimensional operators • For width, Need higher twist contribution

26. Two places to look Reconstruction of Imaginary Correlator and RAA from RHIC

27. Y’ Reconstruction of Imaginary correlator • Imaginary correlator r J/y w m S0 • Reconstructed correlator

28. Morita, Lee (09) arXiv:0908.2856

29. 2-comp model (Rapp) Comparison with experimental data of RHIC (√s=200 GeV at midrapidity)T. Song, SHLee (preliminary) Melting of y’ cc Slope: GJ/y Melting T of J/y Height: mass of J/y

30. Effects of width and mass Assumed recombination effect to be the same Mass shift by -100 MeV • At LHC

31. Applications for mass shift in nuclear matter

32. Anti proton Heavy nuclei Expected luminosity at GSI2x 1032cm-2s-1 Observation of Dm through p-A reaction at PANDA Can be done at J-PARC

33. Summary • Nuclear matter: non trivial change characteristic of QCD phase transition • 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/y, cc to change mass of 7, 15 MeV .  Larger effect for y(3686), y(3770) 4. Such effects could be searched at FAIR, J-PARC