1. EOS in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach
Takashi Umeda (Hiroshima Univ.)
for WHOT-QCD Collaboration
Lattice 2010, Sardina, Italy, June 2010
Lattice 2010
T. Umeda (Hiroshima)
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2. QCD Thermodynamics on the lattice
Most studies done with staggerd-type quarks
less computational costs
a part of chiral sym. preserved ...
 Nf=2+1, almost physical quark mass, μ≠0
4th-root trick to remove unphysical “tastes”
 non-locality “universality is not guaranteed”
It is important to cross-check with
theoretically sound lattice quarks like Wilson-type quarks
Most of this talk is not so recent studies
Our aim is to investigate
QCD Thermodynamics with Wilson-type quarks
WHOT-QCD Collaboration
Lattice 2010
T. Umeda (Hiroshima)
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3. Fixed scale approach to study QCD thermodynamics
Temperature T=1/(Nta) is varied by Nt at fixed a
safe region ?
integral method needs low T (p=0)
303
153
603
753
453
(3fm/a)3 =
Advantages
- Line of Constant Physics
- T=0 subtraction for renorm.
(spectrum study at T=0 )
- larger 1/a in whole T region
Disadvantages
- T resolution by integer Nt
　 - Statistics in lower T region
- coding for odd Nt
Most of this talk is not so recent studies
fixed scale approach
Lattice 2010
T. Umeda (Hiroshima)
/14

4. T-integration method to calculate the EOS
We propose a new method (“T-integration method”)
to calculate the EOS at fixed scales
T.Umeda et al. (WHOT-QCD), Phys.Rev.D79 (2009) (R)
Our method is based on the trace anomaly (interaction measure),
Most of this talk is not so recent studies
and the thermodynamic relation.
Lattice 2010
T. Umeda (Hiroshima)
/14

5. Test in quenched QCD Our results are roughly
consistent with previous results.
Our results deviate from the
fixed Nt=8 results [*]
at higher T ( aT~0.3 or higher )
Trace anomaly is sensitive to
spatial volume at lower T
(below Tc).
V > (2fm)3 is ncessarry.
Most of this talk is not so recent studies ~
[*] G. Boyd et al., NPB469, 419 (1996)
Lattice 2010
T. Umeda (Hiroshima)
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6. T=0 & T>0 configurations for Nf=2+1 QCD
T=0 simulation: on 283 x 56 by CP-PACS/JLQCD Phys. Rev. D78 (2008)
- RG-improved Iwasaki glue + NP-improved Wilson quarks
- β=2.05, κud=0.1356, κs=0.1351
- V~(2 fm)3 , a=0.07 fm,
- configurations available on the ILDG/JLDG
T>0 simulations: on 323 x Nt (Nt=4, 6, ..., 14, 16) lattices
RHMC algorithm, same parameters as T=0 simulation
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)
/14

7. Formulation for Nf=2+1 improved Wilson quarks
Phys. Rev. D73,
CP-PACS/JLQCD
Most of this talk is not so recent studies
Noise method ( #noise = 1 for each color & spin indices )
Lattice 2010
T. Umeda (Hiroshima)
/14

8. Beta-functions from CP-PACS/JLQCD results
Trace anomaly needs Beta-functions in Nf=2+1 QCD
Direct fit method Phys. Rev. D64 (2001)
Most of this talk is not so recent studies
fit β,κud,κs as functions of
with fixed
Lattice 2010
T. Umeda (Hiroshima)
/14

9. Beta-functions from CP-PACS/JLQCD results
Meson spectrum by CP-PACS/JLQCD Phys. Rev. D78 (2008)
3 (β) x 5 (κud) x 2 (κs) = 30 data points
fit β,κud,κs as functions of
Most of this talk is not so recent studies
χ2/dof=1.6
χ2/dof=2.1
χ2/dof=5.3
only statistical error
Lattice 2010
T. Umeda (Hiroshima)
/14

10. Trace anomaly in Nf=2+1 QCD
T[MeV]
Nt config. (x 5MD traj.)
Sg Sq
(*)
Preliminary
Most of this talk is not so recent studies
(*) T=0 (Nt=56) by CP-PACS/JLQCD
Sg calculated with 6500traj.
Lattice 2010
T. Umeda (Hiroshima)
/14

11. Trace anomaly in Nf=2+1 QCD
T[MeV]
Preliminary p4
asqtad
Most of this talk is not so recent studies
HotQCD PRD80,014504(2009)
stout
peak height ~ 5-7
in KS results
( mq ~ mqphys. )
peak height  small
as Nt  large
HISQ
Aoki et al. JHEP01,089(2006)
HotQCD arXiv
Lattice 2010
T. Umeda (Hiroshima)
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12. Quark mass dependence of Trace anomaly
0.05ms
Most of this talk is not so recent studies
HotQCD PRD91,054504(2010)
CP-PACS
PRD64, (2001)
peak height of the Trace anomaly
 small quark mass dependence
peak position shifts slightly.
Our result seems to be reasonable !
0.2ms
HotQCD arXiv
Lattice 2010
T. Umeda (Hiroshima)
/14

13. Equation of State in Nf=2+1 QCD
Preliminary
T-integration
is performed by the trapezoidal
rule.
ε/T4 is calculated from
Large error in whole T region
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)
/14

14. Summary & outlook
We presented the EOS in Nf=2+1 QCD using improve Wilson quarks
Beta functions
More work needed
Reweighting method ?
Equation of state
More statistics needed in the lower temperature region
Nf=2+1 QCD just at the physical point
the physical point (pion mass ~ 140MeV) by PACS-CS
Finite density
We can combine our approach with the Taylor expansion method,
to explore EOS at μ≠0
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)
/14

15. Back-up slides Most of this talk is not so recent studies Lattice 2010
T. Umeda (Hiroshima)

16. A systemtic error To calc. Beta-functions fit β,κud,κs as functions of
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)

17. Beta-functions from CP-PACS/JLQCD results
Meson spectrum by CP-PACS/JLQCD Phys. Rev. D78 (2008)
χ2/dof~2
χ2/dof~2
χ2/dof~5
Most of this talk is not so recent studies
fit β,κud,κs as functions of
Lattice 2010
T. Umeda (Hiroshima)

18. Beta-functions from CP-PACS/JLQCD results
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)

19. Trace anomaly (β&κ derivative part)
Most of this talk is not so recent studies
Lattice 2010
T. Umeda (Hiroshima)