23 Jun. 2010Kenji Morita, GSI / XQCD20101 Mass shift of charmonium near QCD phase transition and its...

23 Jun. 2010 Kenji Morita, GSI / XQCD2010 1

Mass shift of charmonium near Mass shift of charmonium near QCD phase transition and its QCD phase transition and its

implication to relativistic heavy implication to relativistic heavy ion collisionsion collisions

Kenji Morita Kenji Morita (GSI) (GSI) in Collaboration with in Collaboration with

Su Houng Lee (Yonsei Univ.)Su Houng Lee (Yonsei Univ.)

Gluon condensates in the hadronic environment near phase boundary

Mass shift of J/ and c from QCDSR

Possible influences in statistical production


Our ApproachOur ApproachQCD sum rules with temperature dependent gluon condensatesQCD sum rules with temperature dependent gluon condensates

Condensates　　　　　　Spectral density

So far, pure gauge only

Gluon Condensates from lQCD

Dispersion relation + OptimizationOPE for 2-point

correlator

K.M and Lee, PRL100,PRC77,0908.2856


Gluon condensates in full Gluon condensates in full QCDQCD

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


Implication from Nuclear Implication from Nuclear MatterMatterNuclear matter : full QCDNuclear matter : full QCD

Linear density approximation

Chiral Limit→Subtracting fermionic termMoment of gluon distribution function

→Picking up gluonic contribution

Cohen et al, PRC‘92

Klingl et al, PRL’99

Hayashigaki PTP’99

Density-dep. part


A Model for Gluon A Model for Gluon CondensatesCondensates

Extend previous expression to a resonance Extend previous expression to a resonance gas (w/ excluded volume correction)gas (w/ excluded volume correction)

Requirement : reproducing lattice EoS below Requirement : reproducing lattice EoS below TTcc with relevant hadronic degrees of with relevant hadronic degrees of freedomfreedom


mmii00

Hadron masses in the chiral limitHadron masses in the chiral limit SU(3)

AGi =0.9: assumed to be common


Fit to lattice dataFit to lattice data22 fit of v fit of v00 to EoS and Scalar condensate to EoS and Scalar condensate

v0 = 0.543±0.076 2/dof = 8.99

= 0.393±0.042 2/dof = 11.51

= 0.183±0.016 2/dof = 23.41

Data: Bazavov et al., PRD80

Caveat :

Finer lattice spacing /

physical quark mass

may fit better with v0=0

cf. Nt=12, Budapest-Wuppertal

talk by P.Huovinen


Gluon condensates : resultsGluon condensates : results

Chemical potential leads to larger change of the gluon condensates

Lager mass shift in lower collision energy

(Andronic et al, NPA772)


Borel sum rule analysisBorel sum rule analysis

Flattest

Mmin : 30% Power corr.Mmax : 70% Pole dominance

T=156 MeV

B=403 MeV

v0=0


JJ//andandcc in hadronic matter in hadronic matter


JJ//andandcc in hadronic matter in hadronic matterRegarding v0=0 (0.54) as maximum (minimum)

10-50 MeV for J/

20-100 MeV for c

Largest at the smallest sNN

due to largest B


Charmonium ratio from stat. Charmonium ratio from stat. modelmodel

Independent of # of c-quarkIndependent of # of c-quark’ mass shift : unknown from QCDSR

2nd order Stark effect:

53 ~ 155 MeV

Consistent with experimental data

for small shift

J/ coming from c


SummarySummary

Modeling gluon condensates with Modeling gluon condensates with hadron gas : valid up to Thadron gas : valid up to T~~180 MeV180 MeVSizable mass shifts at freeze-out Sizable mass shifts at freeze-out points : from QCDSRpoints : from QCDSRLarger mass shift at high baryon Larger mass shift at high baryon densitydensityMass-shifted charmonium Mass-shifted charmonium generation via statistical generation via statistical hadronization may probe it.hadronization may probe it.


BackupBackup


Heavy Quarkonium as a Heavy Quarkonium as a Probe of DeconfinementProbe of Deconfinement

Heavy quarks : Heavy quarks : mmcc ～～ 1.5GeV, 1.5GeV, mmbb ～～ 4.7GeV 4.7GeV >> >> QCDQCD

No chiral symmetryQQbar states bound by

confinement force Successful description

by Coulomb+linear

potential

Change of the property : change of confinement property


Simplest model : free gasSimplest model : free gas

Only two parameters : Only two parameters : TT and and bb

Strangeness neutrality

Isospin symmetric matter

Other quantities follow from thermodynamicsOther quantities follow from thermodynamics


Excluded volume correctionExcluded volume correctionReminder : Van-der-Waals EoSReminder : Van-der-Waals EoSRischke et al (’91): keep thermodynamic Rischke et al (’91): keep thermodynamic consistencyconsistency

Effectively, chemical potential is reduced→Repulsive interaction

(Omitting technical detail here)


Excluded volume correctionExcluded volume correctionCorrected thermo. quantities : follow from Corrected thermo. quantities : follow from usual thermo. relationsusual thermo. relations

vv00 is related to hard-core radius is related to hard-core radius

rh = 0.3-0.5 fm → v0 = 0.5-2 fm3


Effective coupling constantEffective coupling constantLattice measurement in Full QCDLattice measurement in Full QCD

Determined by force between static heavy quark-antiquark

Kaczmarek and Zantow, PRD71 ’05

Caveat : Nf=2, Tc=202 MeV

Fit with bezier interpolation


Borel Transformation in QCDSRBorel Transformation in QCDSRLarge Large QQ22 limit + Probing resonance (large n) limit + Probing resonance (large n)

Suppression of high energy part of (s)

Solve

Dispersion relation=


Dispersion relationDispersion relation

qq22 << 0 0

Intermediate states can be described as short-distant

phenomena


Statistical production of Statistical production of Heavy quarks?Heavy quarks?

Statistical hadronization can account for the charm-charm ratio only in AA case.

Andronic et al, PLB678


Chemical freeze-out near Chemical freeze-out near the phase boundary?the phase boundary?

Implications:

• Hadronization at phase boundary from thermalized QGP

• Freeze-out just after hadronization

(Andronic et al, NPA772) Spectral change?


Looking for in-medium Looking for in-medium effecteffect

QCDSR approach : gluon condensates governQCDSR approach : gluon condensates govern

How to estimate gluon condensates in hadronic matter?


Early WorksEarly Works


Gluon condensatesGluon condensatesFor pure gluonic system [SU(3)]For pure gluonic system [SU(3)]

We connected them with energy density and pressure

and p can be obtained from lattice simulation

=M0

→M2

Both > 0

Characterizing Gluonic sector


Sum rule constraintsSum rule constraints

From the OPE...From the OPE...

m s0

f

T↑

Increase

If other quantities are fixed:

• m : decrease

• : Increase

• s : decrease

• f : Increase

23 Jun. 2010Kenji Morita, GSI / XQCD20101 Mass shift of charmonium near QCD phase transition and its...

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