yu maezawa (univ. of tokyo) in collaboration with s. aoki, k. kanaya, n. ishii, n. ukita,
DESCRIPTION
Thermodynamics of QCD in lattice simulation with improved Wilson quark action at finite temperature and density. WHOT-QCD Collaboration. Yu Maezawa (Univ. of Tokyo) in collaboration with S. Aoki, K. Kanaya, N. Ishii, N. Ukita, T. Umeda (Univ. of Tsukuba) T. Hatsuda (Univ. of Tokyo) - PowerPoint PPT PresentationTRANSCRIPT
Thermodynamics of QCD Thermodynamics of QCD in lattice simulation in lattice simulation
with improved Wilson quark action with improved Wilson quark action at finite temperature and density at finite temperature and density
Yu Maezawa (Univ. of Tokyo)Yu Maezawa (Univ. of Tokyo)
in collaboration within collaboration with
S. Aoki, K. Kanaya, N. Ishii, N. Ukita, S. Aoki, K. Kanaya, N. Ishii, N. Ukita, T. Umeda (Univ. of Tsukuba)T. Umeda (Univ. of Tsukuba)T. Hatsuda (Univ. of Tokyo)T. Hatsuda (Univ. of Tokyo)
S. Ejiri (BNL)S. Ejiri (BNL)
WHOT-QCD CollaborationWHOT-QCD Collaboration
xQCD @ INFN, Aug. 6-8, 2007
In part published in PRD 75 (2007) 074501 and J. Phys. G 34 (2007) S651
Y. Maezawa @ xQCD2007 2
1, Many properties at T=0 have been well-investigated RG-improved gauge action + Clover-improved Wilson action by CP-PACS Collaboration (2000-2001)
Accurate study at T≠0 are practicable
2, Most of studies at T≠0 have been done with Staggered quark action Studies by Wilson quark action are important
IntroductionFull-QCD simulation on lattice at finite T and q
important from theoretical and experimental veiw
We perform simulations with the Wilson quark action, because
3
Previous studies at T ≠ 0 , q = 0 with Wilson quark action (CP-PACS, 1999-2001)
- phase structure, Tc, O(4) scaling, equation of state, etc.
Previous studies at T ≠ 0 , q = 0 with Wilson quark action (CP-PACS, 1999-2001)
- phase structure, Tc, O(4) scaling, equation of state, etc.
Introduction
This talk Finite q using Taylor expansion method
Quark number susceptibility & critical point
Fluctuation at finite q
Heavy-quark potential in QGP medium
Heavy-quark free energy
Y. Maezawa @ xQCD2007 4
Lattice size:
Action: RG-improved gauge action + Clover improved Wilson quark action
Quark mass & Temperature (Line of constant physics)
# of Configurations: 500-600 confs. (5000-6000 traj.) by Hybrid Monte Carlo algorithm
Lattice spacing (a) near Tpc
fm 25.0~ ,/1 aaNT t
Two-flavor full QCD simulationTwo-flavor full QCD simulation
Numerical Simulations
41633 ts NN
points) (12 0.376.0 :80.0/
points) (13 0.482.0 :65.0/
cc
cc
TTTmm
TTTmm
~
~
Y. Maezawa @ xQCD2007 5
1, Heavy-quark free energy1, Heavy-quark free energyHeavy-quark “potential” in QGP mediumDebye screening mass
6
Debye mass and
relation to p-QCD at high T
Heavy-quark free energy at finite T and q Heavy-quark free energy at finite T and q
Heavy quark free energy in QGP matter Channel dependence of heavy-quark “potential”
( 1c, 8c, 3c, 6c) Debye screening mass at finite T
Finite density (q≠ 0)
Maezawa et al.RPD 75 (2007) 074501
In Taylor expantion method,
c.f.) Doring et al.EPJ C46 (2006) 179
in p4-improved staggered action
Free energies between Q-Q, and Q-Q at q > 0 ~
7
)(4 nUt
Static charged quark
Polyakov loop:
Separation to each channel after Coulomb gauge fixing
Taylor expansion
Normalized free energy of the quark-antiquark pair (Q-Q "potential")
Q-Q potential:
Q-Q potential:
Heavy-quark free energy at finite T and q
Y. Maezawa @ xQCD2007 8
QQ potential at QQ potential at T > TcQQ potential at QQ potential at T > Tc
1c channel: attractive force
8c channel: repulsive force
become weakat q > 0~
9
QQ potential QQ potential at at T > TcQQ potential QQ potential at at T > Tc
3c channel: attractive force6c channel: repulsive force
become strongat q > 0~
10
Debye screening effectDebye screening effectDebye screening effectDebye screening effectPhenomenological
potential Screened Coulomb form
: Casimir factor
(T, q) : effective running coupling
mD(T, q) : Debye screening mass
Assuming, 2210 ))(()()(),(
TT
TTTT qq
q
220 ))(()(),( ,, T
TmTmTm qDDqD
Y. Maezawa @ xQCD2007 11
Substituting and mD to V(r, T,q)
and comparing to v0(r, T), v1(r, T) … order by order ofq/T
Debye screening effectDebye screening effectDebye screening effectDebye screening effect
Debye screening mass (mD,0 , mD,2 ) at finite q
Fitting the potentials of each channel
with i and mD,i as free parameters.
Y. Maezawa @ xQCD 2007 12
• Channel dependence of mD disappear at T > 2.0Tc
cTT
Debye screening effectDebye screening effectDebye screening effectDebye screening effect
cTT
~
Channel dependence of mD,0(T) and mD,2(T)
13
cTT
2
0
12
02 lnlnln)(
SMSM
Tg
MeV 2612 fNSM
2
2
26
2loop-2
221)()( q
NN
Dff TTgTm
Leading order thermal perturbation
2-loop running coupling on a lattice vs. perturbative screening mass
)(TmD
TTT 3,2,
T T2 T3
Lattice screening mass is not reproduced
by the LO-type screening mass.
cTT
14
TTgCm mmag )(2Magnetic screening mass:
)(ln)()(
)(, 2
6
60
2
12
1
1
2
311 go
m
mTgTg
T
Tm
mag
DN
NNLOD
f
f
Next-to-leading order perturbation at q = 0
Rebhan, PRD 48 (1993) 48
on a lattice vs. perturbative screening mass
)(TmD
482.0mC Quenched resultsNakamura, Saito and Sakai (2004)NLO-type screening
mass lead to a better agreement
with the lattice screening mass.
cTT
T T2 T3
?,NLO
2Dm
Y. Maezawa @ xQCD2007 15
2, Fluctuation at finite 2, Fluctuation at finite q
Quark number susceptivilityIsospin susceptivility
16
Fluctuation at finite q
Critical point at q > 0 have been predicted
T
hadron
QGP
CSCIn numerical simulations
Quark number and isospin susceptibilities
2I
2
I
2q
2
32q
2
q
ln1
p
Z
VT
p
2
2
duI
duq
• q has a singularity
• I has no singularity
At critical point:
Hatta and Stephanov, PRL 91 (2003) 102003
Taylor expansion of quark number susceptibility
2
q422
42
2
q 122T
ccT
Tp
T q
Nf = 2, mq > 0: Crossover PT at q = 0
17
Susceptibilities at q = 0
• Susceptibilities (fluctuation) at q = 0 increase rapidly at Tpc
• I at T <Tpc is related to pion fluctuoation
2
q422
42
2122
Tcc
T
Tp
T q
q
Taylor expansion:Taylor expansion:
RG + Clover Wilson RG + Clover Wilson
I at m/m = 0.65 is larger than 0.80
65.0/ mm 80.0/ mm
= 2c2
= 2c2
I
= 2c2
= 2c2
I
18
Susceptibilities at q > 0
• Second derivatives: Large spike for q near Tpc.
Dashed Line: 9q, prediction by hadron resonance gas model
2
q422
42
2122
Tcc
T
Tp
T q
q
Taylor expansion:Taylor expansion:
= 4!c4
= 4!c4
I
Large enhancement in the fluctuation of baryon number (not in isospin) around Tpc as q increases: Critical point?
~
65.0/ mm 80.0/ mm
= 4!c4
= 4!c4
I
Y. Maezawa @ xQCD 2007 19
Comparison with Staggered quark resultsComparison with Staggered quark resultsQuark number (q) and Isospin (I) susceptibilities
p4-improved staggered quark , Bielefeld-Swqnsea Collaboration, Phys. Rev. D71, 054508 (2005)
• Similar results have been obtained with Staggered quark action
Lattice QCD suggests large fluctuation of q at q > 0~
Y. Maezawa @ xQCD2007 20
SummarySummarySummarySummaryWe study QCD thermodynamics in lattice simulations with two flavors of improved Wilson quark action
Heavy-quark free energy Fluctuation at finite q
Heavy-quark free energy
QQ potential: become weakQQ potential: become strong
1c, 3c channel: attractive force8c, 6c channel: repulsive force
at q = 0
at q > 0~
LO2,2,
NLO0,0, ,~ DDDD mmmm Debye screening mass:
?NLO2,Dm
Fluctuation at finite q
Large enhancement in the fluctuation of baryon number
around Tpc as q increaseIndication of critical point at q > 0 ?