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Heavy quark and quarkonia at finite temperature
Péter Petreczky
Physics Department and RIKEN-BNL
xQCD 2008, NCSU, July 21-23, 2008
• Introduction : Deconfinement at high temperature and color screening
• Quarkonium correlators and spectral functions from lattice
• Quarkonium spectral functions in potential models
• Effective field theory approach for heavy quark bound states
• Static meson correlators T>0 in Euclidean time
• Conclusions and Outlook
RBC-Bielefeld Collaboration
Color screening in QCD and quarkonia melting
Does this imply quarkonium melting ?
Matsui and Satz PLB 178 (86) 416
see also
Digal et al, PLB 514 (01) 57 ; PRD 64 (01) 094015,
),(),(),(,)0,0(),(),,( 3 xqxqxJJxJexdTpG HHHH
xpi
Meson correlators and spectral functions
5,,5,1H
)(),( iDTG
Imaginary time Real time
0 ))2/(sinh(
))2/(1(cosh(),(),(
T
TTdTG
LGT
Experiment, dilepton rate)()(Im
1
2
)()(
RDDD
MEM),,( TpG ),,( Tp
Quarkonium spectral functions above deconfinement
E.g. free theory :
P.P., Teaney, PRD 73 (2006) 014508
interactions :
calculate the area under the peak using
lattice QCD !
quark number susceptibility
+
If there is no T-dependence in the spectral
function,
0 ))2/(sinh(
))2/(1(cosh(),(),(
T
TTdTG
temperature dependene of ),( TG
Charmonia correlators at T>0
Datta et al, PRD 69 (04) 094507
Charmonia correlators at T>0
zero mode contribution is not present in the time derivative of the correlatorUmeda, PRD 75 (2007) 094502
Datta, P.P., Quark Matter 2008, arXiv:0805.1174
Charmonia correlators at T>0
zero mode contribution is not present in the time derivative of the correlatorUmeda, PRD 75 (2007) 094502
Datta, P.P., Quark Matter 2008, arXiv:0805.1174
Estimating the zero mode contribution
vector axial-vector
Heavy quark susceptibility in quasi-particle picture
Zero mode contribution in quasi-particle picture
Datta, P.P., Quark Matter 2008, arXiv:0805.1174
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506
Charmonium spectral functions at finite temperature
no large T-dependence but details are not resolved
1
m2 V (
r ) E
GNR(
r ,
r ',E) 3(
r
r ')
E 2Nc
ImGNR
r ,r ',E
r r '0
E 2Nc
1
m2
'ImGNR
r ,r ',E
r r '0
S-wave
P-wave
many gluon exchanges important near threshold
Quarkonium spectral functions in potential models
pert 2 3
8111
3s
+
~ MJ/ , s0 nonrelativistic s0 perturbative
PRD77 (08) 014501, EPJC ST 155 (08) 101 Mócsy, P.P., PRL 99 (07) 211602,
use lattice data on the quark anti-quark free energy to construct the potential
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement above free case indication of correlations
c
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement above free case indication of correlations
• height of bump in lattice and model are similar
•The correlators do not change significantly despitethe melting of the bound states
c
• all P-states disappear already by 1.2Tc
but the derivatives of the of the correlators don not show any significant T-dependence
bc ,
Effective field theory approach for heavy quark bound states
Brambilla, Ghiglieri, P.P., Vairo arXiv:0804.0993 [hep-ph]
The heavy quark mass provides a hierarchy of different energy scales
there are also different thermal scales in the weak coupling regime
potential is the matching parameter of EFT !
singlet-octet transition : Landau damping :
Brambilla, Ghiglieri, P.P., Vairo arXiv:0804.0993 [hep-ph]
pNRQCD at finite temperature for static quarks
static limit : LO in 1/m -expansion
EFT for energy scale
If there are thermal contribution to the potentials
The potential for :
The potential for :
The potential for :
Laine, Philipsen, Romatschke, Tassler, JHEP 073 (2007) 054
Static meson correlators in SU(N) gauge theory
cyclic Wilson loops, Laine, Philipsen, Romatschke, Tassler, JHEP 073 (‘07) 054
Jahn, Philipsen, PRD 70 (’04) 074504
Numerical results in SU(2) gauge theory
Bazavov, P.P., Velytsky arXiv:0807.xxxx [hep-lat]
( adjoint triplet )
Summary and outlook
• The temperature dependence of quarkonium correlators in Euclidean time
is dominated by the zero mode contribution and are not sensitive to the change
in the spectral function related to melting of the bound states
• The zero mode contribution can be very well described by a quasi-particle model
• Potential models at finite temperature predict melting of all charmonium states,
yet are consistent with lattice data on the Eulcidean correlators
• In the weak coupling regime potential models at T>0 can be justified in the
EFT framework, however T>0 the potential has an imaginary part;
for r < Debye radius the thermal corrections go like powers of r
for r > Debye radius the real part of the potential is exponentially screened
• Static mesons correlators at T>0 can be studied in lattice QCD and indicate
survival of singlet states smaller than ~0.5/T and melting of octet states
Back-up slides
Juge et al, hep-lat/0103008
The color octet correlator only fixes the relative color orientation of static
quark anti-quark pair.
Perturbative relation between
to the color singlet free energy at high
temperatures