23 Jun. 2010Kenji Morita, GSI / XQCD20101 Mass shift of charmonium near QCD phase transition and its implication to relativistic heavy ion collisions Kenji.

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Presentation transcript:

23 Jun. 2010Kenji Morita, GSI / XQCD20101 Mass shift of charmonium near QCD phase transition and its implication to relativistic heavy ion collisions Kenji Morita (GSI) in Collaboration with Su Houng Lee (Yonsei Univ.) Gluon condensates in the hadronic environment near phase boundary Mass shift of J / y and c c from QCDSR Possible influences in statistical production

23 Jun. 2010Kenji Morita, GSI / XQCD20102 Our Approach QCD sum rules with temperature dependent gluon condensates Condensates Spectral density So far, pure gauge only Gluon Condensates from lQCD Dispersion relation + Optimization OPE for 2-point correlator K.M and Lee, PRL100,PRC77,

23 Jun. 2010Kenji Morita, GSI / XQCD20103 Gluon condensates in full QCD In full QCD... In full QCD... Additional quark contribution appears  and p can be obtained from lattice, but they contain the quark contribution also We want  and p of gluonic sector

23 Jun. 2010Kenji Morita, GSI / XQCD20104 Implication from Nuclear Matter Nuclear matter : full QCD Linear density approximation Chiral Limit→Subtracting fermionic term Moment of gluon distribution function →Picking up gluonic contribution Cohen et al, PRC‘92 Klingl et al, PRL’99 Hayashigaki PTP’99 Density- dep. part

23 Jun. 2010Kenji Morita, GSI / XQCD20105 A Model for Gluon Condensates Extend previous expression to a resonance gas (w/ excluded volume correction) Requirement : reproducing lattice EoS below T c with relevant hadronic degrees of freedom

23 Jun. 2010Kenji Morita, GSI / XQCD20106 mi0mi0mi0mi0 Hadron masses in the chiral limit Hadron masses in the chiral limit SU(3) A G i =0.9 : assumed to be common

23 Jun. 2010Kenji Morita, GSI / XQCD20107 Fit to lattice data c 2 fit of v 0 to EoS and Scalar condensate v 0 = 0.543±0.076 c 2 /dof = 8.99 = 0.393±0.042 c 2 /dof = = 0.183±0.016 c 2 /dof = Data: Bazavov et al., PRD80 Caveat : Finer lattice spacing / physical quark mass may fit better with v 0 =0 cf. N t =12, Budapest-Wuppertal talk by P.Huovinen

23 Jun. 2010Kenji Morita, GSI / XQCD20108 Gluon condensates : results Chemical potential leads to larger change of the gluon condensates Lager mass shift in lower collision energy (Andronic et al, NPA772)

23 Jun. 2010Kenji Morita, GSI / XQCD20109 Borel sum rule analysis Flattest M min : 30% Power corr. M max : 70% Pole dominance T=156 MeV m B =403 MeV v 0 =0

23 Jun. 2010Kenji Morita, GSI / XQCD J / y and c c in hadronic matter

23 Jun. 2010Kenji Morita, GSI / XQCD J / y and c c in hadronic matter Regarding v 0 =0 (0.54) as maximum (minimum) MeV for J / y MeV for c c Largest at the smallest s NN due to largest m B

23 Jun. 2010Kenji Morita, GSI / XQCD Charmonium ratio from stat. model Independent of # of c-quark y ’ mass shift : unknown from QCDSR 2 nd order Stark effect: 53 ~ 155 MeV Consistent with experimental data for small shift J / y coming from c c

23 Jun. 2010Kenji Morita, GSI / XQCD201013Summary Modeling gluon condensates with hadron gas : valid up to T ~ 180 MeV Sizable mass shifts at freeze-out points : from QCDSR Larger mass shift at high baryon density Mass-shifted charmonium generation via statistical hadronization may probe it.

23 Jun. 2010Kenji Morita, GSI / XQCD Backup

23 Jun. 2010Kenji Morita, GSI / XQCD Heavy Quarkonium as a Probe of Deconfinement Heavy quarks : m c ～ 1.5GeV, m b ～ 4.7GeV >> L QCD No chiral symmetry QQbar states bound by confinement force Successful description by Coulomb+linear potential Change of the property : change of confinement property

23 Jun. 2010Kenji Morita, GSI / XQCD Simplest model : free gas Only two parameters : T and m b Only two parameters : T and m b Strangeness neutrality Isospin symmetric matter Other quantities follow from thermodynamics Other quantities follow from thermodynamics

23 Jun. 2010Kenji Morita, GSI / XQCD Excluded volume correction Reminder : Van-der-Waals EoS Rischke et al ( ’ 91): keep thermodynamic consistency Effectively, chemical potential is reduced →Repulsive interaction (Omitting technical detail here)

23 Jun. 2010Kenji Morita, GSI / XQCD Excluded volume correction Corrected thermo. quantities : follow from usual thermo. relations v 0 is related to hard-core radius r h = fm → v 0 = fm 3

23 Jun. 2010Kenji Morita, GSI / XQCD Effective coupling constant Lattice measurement in Full QCD Determined by force between static heavy quark-antiquark Kaczmarek and Zantow, PRD71 ’05 Caveat : N f =2, T c =202 MeV Fit with bezier interpolation

23 Jun. 2010Kenji Morita, GSI / XQCD Borel Transformation in QCDSR Large Q 2 limit + Probing resonance (large n) Suppression of high energy part of r (s) Solve Dispersion relation =

23 Jun. 2010Kenji Morita, GSI / XQCD Dispersion relation Problem : How to obtain QCD is an asymptotic free theory = P ( q 2 ) is calculable if a s ( q 2 ) is small where? Q 2 = -q 2 > 0 q2 < 0q2 < 0q2 < 0q2 < 0 Intermediate states can be described as short-distant phenomena

23 Jun. 2010Kenji Morita, GSI / XQCD Statistical production of Heavy quarks? Statistical hadronization can account for the charm-charm ratio only in AA case. Andronic et al, PLB678

23 Jun. 2010Kenji Morita, GSI / XQCD Chemical freeze-out near the phase boundary? Implications: Hadronization at phase boundary from thermalized QGP Freeze-out just after hadronization (Andronic et al, NPA772) Spectral change?

23 Jun. 2010Kenji Morita, GSI / XQCD Looking for in-medium effect QCDSR approach : gluon condensates govern How to estimate gluon condensates in hadronic matter?

23 Jun. 2010Kenji Morita, GSI / XQCD Early Works Change of confinement potential : Mass shift of J / y etc Change of confinement potential : Mass shift of J / y etc (Hashimoto et al., ’86) Debye screening in QGP : No bound state can exist in QGP – J / y suppression (Matsui-Satz ’86)

23 Jun. 2010Kenji Morita, GSI / XQCD Gluon condensates For pure gluonic system [SU(3)] We connected them with energy density and pressure  and p can be obtained from lattice simulation =M0=M0 →M2→M2 Both > 0 Characterizing Gluonic sector

23 Jun. 2010Kenji Morita, GSI / XQCD Sum rule constraints From the OPE... m 2,  s0s0 f T↑T↑ Increase If other quantities are fixed: m 2 : decrease  : Increase s 0 : decrease f : Increase