1. Free Energies of Heavy Quarks in Full-QCD Lattice Simulations with Wilson-Type Quark Action
WHOT-QCD Collaboration
Yu Maezawa (RIKEN)
in collaboration with
S. Aoki, K. Kanaya, N. Ishii, H. Ohno (Univ. of Tsukuba)
S. Ejiri (BNL)
T. Hatsuda (Univ. of Tokyo)
T. Umeda (YITP)
QUARK Knoxville, Mar. 31, 2009

2. Introduction
To remove theoretical uncertainties in heavy-ion experiments
First principle calculations by Lattice QCD at finite (T, m): important
Purpose of WHOT-QCD Collaboration
Investigation of QCD thermodynamics
in lattice simulations with Wilson quark action
e.g.) critical temperature, phase structure, equation of state,
charmonium spectra, heavy-quark free energy, Debye mass,…
Why Wilson quark action?
Basic properties at T = 0 well investigated by CP-PACS&JLQCD Coll.:
Iwasaki (RG) improved gauge action + Clover improved Wilson quark action
Precise set of the lattice spacing and quark mass is
applicable at finite T based on the fixed scale approach.
talk by Kanaya on Friday
Topics of this talk
Heavy-quark free energy
Relation of inter-quark interaction between zero and finite T
Debye screening effect in QGP
perturbative Debye mass and flavor dependence

3. Operator similar to the Wilson-loop
Heavy-quark free energy
To characterize an interaction b/w static quarks,
T = 0
Heavy-quark potential
Wilson-loop operator
T > 0
Heavy-quark free energy Nadkarni (1986)
Polyakov-line : static quark at x
Correlation b/w Polyakov-lines projected to a color singlet channel in the Coulomb gauge
Operator similar to the Wilson-loop
at finite T
Heavy-quark free energy may behave in QGP as:
short r: F 1(r,T ) ~ V(r) (no effect from thermal medium)
mid r : screened by plasma
long r : two static-quark free energies w/o interactions

4. Approaches of lattice simulations at finite T
To vary temperature on the lattice,
a: lattice spacing
Nt: lattice size in E-time direction
Fixed Nt approach
Fixed scale approach WHOT-QCD, PRD 79 (2009) talk by Kanaya on Friday
Changing a (controlled by the gauge coupling (b = 6/g2)), fixing Nt
Advantages: T can be varied arbitrarily, because b is an input parameter.
Changing Nt , fixing a
Advantages: investigation of T dependence w/o changing spatial volume possible.
renormalization factor dose not change when T changes.

5. Results of numerical simulations
Heavy-quark potential at T = 0 from Wilson-loop operator
Heavy-quark free energy at T > 0 from Polyakov-line correlator
Properties of Debye screening mass

6. Simulation details Nf = 2+1 full QCD simulations
Lattice size: Ns3 x Nt = 323 x 12, 10, 8, 6, 4
Temperature: T ~ MeV (5 points)
Lattice spacing: a = 0.07 fm
Light quark mass*: mp/mr = (38)
Strange quark mass*: mK/mK* = (28)
Scale setting: Sommer scale, r0 = 0.5 fm
*CP-PACS & JLQCD Coll., PRD78 (2008)

7. Heavy-quark potential at T = 0
Data calculated by
CP-PACS & JLQCD Coll.
on a 283 x 58 lattice
Phenomenological potential
Our fit results
= Coulomb term at short r
+ Linear term at long r
+ const. term

8. Heavy-quark free energy at T > 0
At short distance
F 1(r,T ) at any T
converges to
V(r) = F 1(r,T=0 ).
Short distance physics is
insensitive to T.
Note:
In the fixed Nt approach, this property is used to adjust the constant term of F 1(r,T ).
In our fixed scale approach, because the renormalization is common to all T.
no further adjustment of the constant term is necessary.
We can confirm the expected insensitivity!

9. Heavy-quark free energy at T > 0
At short distance
F 1(r,T ) at any T
converges to
V(r) = F 1(r,T=0 ).
Short distance physics is
insensitive to T.
T ~ 200 MeV: F 1 ~ V up to fm
T ~ 700 MeV: F 1 = V even at 0.1 fm
Range of thermal effect is T-dependent.

10. Heavy-quark free energy at T > 0
2FQ evaluated from
Polyakov-line operator
Long distance
F 1(r,T ) becomes flat and has no increase linealy.
Confinement is destroyed due to a thermal medium effect.
At large r, correlation b/w Polyakov-lines will disappear,
F 1 converges to 2x(static quark free energy) at long distance

11. Derivative of heavy-quark free energy
Derivative screening effect in QGP at mid distance
No screening effect
const. + increasing
Screening effect
decreasing exponentially with r
Screening effect appears obviously
extract the Debye mass by fitting F 1
to screened Coulomb form

12. Debye screening mass in QGP
Temperature dependence of mD
mD is proportional to T.
c.f.) prediction in perturbation theory

13. Debye screening mass in QGP
NLO LO
Perturbative screening mass LO
NLO Rebhan, PRD 48 (1993) 48
Lattice screening mass is not reproduced by LO-type screening mass.
Contribution of NLO-type corrects the LO-type screening mass.

14. Debye screening mass in QGP
Flavor dependence of Debye mass
Nf = 2: fixed Nt ap.
163x4, mp/mr = 0.65
WHOT, PRD75 (2007)
Nf = 0: fixed scale ap.
203x(26-8)
WHOT, in preparation
c.f.) Staggered-type quark action
Tc (Nf=2)
Tc (Nf=0)
Magnitude of Debye mass
RBC-Bielefeld collaboration
Fixed Nt ap., mp ~ 220 MeV
Dynamical quark effects are important for Debye mass.

15. Summary Dynamical quark effects are important for mD.
We report the current status of our study of QCD thermodynamics.
Full-QCD lattice simulations with Wilson-type quark action
in fixed scale approach
Heavy-quark free energy F 1(r,T )
Correlation b/w Polyakov-lines projected to the color-singlet channel in Coulomb gauge
At short distance
F 1 at any T converges to heavy-quark potential at T = 0
Short distance physics is insensitive to T.
At long distance
F 1 becomes flat and has no increase linearly.
Correlation b/w Polyakov-lines disappears and F 1 converges to 2FQ
Debye screening mass in QGP at mid distance
mD is proportional to T well reproduced by perturbative mD in NLO.
Dynamical quark effects are important for mD.