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Thermodynamics of two-flavor Thermodynamics of two-flavor lattice QCD with an improved lattice QCD with an improved

Wilson quark action at Wilson quark action at non-zero temperature and densitynon-zero temperature and density

Yu Maezawa (Univ. of Tokyo)In collaboration with

S. Aoki, K. Kanaya, N. Ishii, N Ukita (Univ. of Tsukuba)T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)

Yu Maezawa (Univ. of Tokyo)In collaboration with

S. Aoki, K. Kanaya, N. Ishii, N Ukita (Univ. of Tsukuba)T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)

WHOT-QCD CollaborationWHOT-QCD Collaboration

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IntroductionIntroductionTo remove theoretical uncertainties in heavy-ion experiments, To remove theoretical uncertainties in heavy-ion experiments,

First principle calculations by Lattice QCD at finite (T, ): importantFirst principle calculations by Lattice QCD at finite (T, ): important

• Many interesting results have been obtained,

e.g. critical temperature, phase structure, equation of state, heavy quark free energies, Debye mass ...

• Many interesting results have been obtained,

e.g. critical temperature, phase structure, equation of state, heavy quark free energies, Debye mass ...

Two key issues for precision lattice studyTwo key issues for precision lattice study

1. Set the lattice spacing and quark mass precisely

2. Understand uncertainties from lattice formulations

1. Set the lattice spacing and quark mass precisely

2. Understand uncertainties from lattice formulations

Accurate calculation of physical quantities at T = 0Accurate calculation of physical quantities at T = 0

Comparison between different fermion formulations is necessary.

e.g. Wilson quark action and Staggered quark action

Comparison between different fermion formulations is necessary.

e.g. Wilson quark action and Staggered quark action

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Why QCD thermodynamics with Wilson Why QCD thermodynamics with Wilson quark action?quark action?1, A well-improved lattice action available: Basic properties at T = 0 well-investigated Iwasaki (RG) improved gauge action + Clover improved Wilson action Systematic studies have been done by CP-PACS Collaboration (1996~). Large stock of data at T = 0

2, Most of studies at T0 have been done using Staggered-type quark actions. Studies by a Wilson-type quark action are necessary.

1, A well-improved lattice action available: Basic properties at T = 0 well-investigated Iwasaki (RG) improved gauge action + Clover improved Wilson action Systematic studies have been done by CP-PACS Collaboration (1996~). Large stock of data at T = 0

2, Most of studies at T0 have been done using Staggered-type quark actions. Studies by a Wilson-type quark action are necessary. Previous studies at T0, q=0 with this action (1999-2001) : phase structure, Tc, O(4) scaling, equation of state, etc.

Previous studies at T0, q=0 with this action (1999-2001) : phase structure, Tc, O(4) scaling, equation of state, etc.Three topics covered in this talkThree topics covered in this talk

Smaller quark mass (Chiral limit)

Smaller lattice spacing (continuum limit)

Finite

Smaller quark mass (Chiral limit)

Smaller lattice spacing (continuum limit)

Finite

Extension to

Extension to

Poster session by Y. MaezawaPoster session by Y. Maezawa

Critical temperature Tc Fluctuations at q > 0 (Quark number susceptibility) Heavy quark free energies and Debye mass in QGP medium

Critical temperature Tc Fluctuations at q > 0 (Quark number susceptibility) Heavy quark free energies and Debye mass in QGP medium

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Lattice spacing (a) near Tc.

Scale setting: meson mass (m)

Lattice spacing (a) near Tc.

Scale setting: meson mass (m)

Simulation detailsSimulation details

Critical temperature Lattice size: Ns3 x Nt = 163 x 4 and 163 x 6, m/m= 0.5 ~ 0.98

Quark number susceptibilities (fluctuations) Lattice size: Ns3 x Nt = 163 x 4, m/m= 0.8, T/Tpc = 0.76 ~ 2.5

Heavy quark free energies and Debye mass Lattice size: Ns3 x Nt = 163 x 4, m/m= 0.65, 0.8, T/Tpc = 1.0 ~ 4.0

Critical temperature Lattice size: Ns3 x Nt = 163 x 4 and 163 x 6, m/m= 0.5 ~ 0.98

Quark number susceptibilities (fluctuations) Lattice size: Ns3 x Nt = 163 x 4, m/m= 0.8, T/Tpc = 0.76 ~ 2.5

Heavy quark free energies and Debye mass Lattice size: Ns3 x Nt = 163 x 4, m/m= 0.65, 0.8, T/Tpc = 1.0 ~ 4.0

1)(/ amNmT t

1/ , ~ 0.25 fm ( 4), 0.17 fm ( 6)t t tT N a a N N

e.g. e.g.

Two-flavor full QCD simulationTwo-flavor full QCD simulation

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1, Critical temperature• Tc from -meson mass m

• Tc from Sommer scale r0

• Tc from -meson mass m

• Tc from Sommer scale r0

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Critical temperature Critical temperature from Polyakov loop from Polyakov loop susceptibilitysusceptibility

)6( MeV (3) (4) 176

)4( MeV (5) )4( 180

Nt

NtTc

TcTc

Chiral extrapolation

Chiral extrapolation

• Ambiguity by the fit ansatz: for the case , Tc becomes 4 MeV higher.

Further simulations with smaller mass are in progress.

• Ambiguity by the fit ansatz: for the case , Tc becomes 4 MeV higher.

Further simulations with smaller mass are in progress.

1

m

mx

2

,)1(

)1(

m

mx

Cx

BxA

m

T

V

pc

Pade-type ansatzPade-type ansatz

Quench limit Chiral limit

Quench limit Chiral limit

2)/( mm

Tpc

/m

Tpc

/m

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Comparison with staggered quark results

Ambiguity of Sommer scale (r0): 10% differencer0 = 0.469(7) fm : A. Gray et al., Phys. Rev. D72, 094507 (2005)

Asqtad improved staggered quark action + Symanzik improved gauge action

r0 = 0.516(21) fm : CP-PACS & JLQCD, hep-lat/0610050Clover improved Wilson quark action + Iwasaki improved gauge action

Studies at T = 0 are also very important for the determination of Tc.

RBC-Bielefeld, hep-lat/0608013 p4-improved staggered quark action RBC-Bielefeld, hep-lat/0608013 p4-improved staggered quark action

Both results seem to approach the same line in the continuum limit (large Nt).

Both results seem to approach the same line in the continuum limit (large Nt).

Tc in Sommer scale unit

Wilson quarkWilson quark

Staggered quark

Staggered quark

0rm

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2, Fluctuations at finite

• Quark number susceptibility• Isospin susceptibility

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Fluctuations at Fluctuations at finite finite Critical point at 0 Critical point at 0

T

hadron

QGP

CSCIn numerical simulations Quark number and isospin susceptibilities

In numerical simulations Quark number and isospin susceptibilities

2I

2

I2q

2

q ,

pp

2

2

duI

duq

Bielefeld-Swansea Collab. (2003) using improved staggered quark action,

Enhancement in the fluctuation of quark number at q > 0 near Tc by Taylor expansion method

Bielefeld-Swansea Collab. (2003) using improved staggered quark action,

Enhancement in the fluctuation of quark number at q > 0 near Tc by Taylor expansion method Confirmation by a Wilson-type

quark actionConfirmation by a Wilson-type quark action

• q has a singularity

• I has no singularity

• q has a singularity

• I has no singularityAt critical

point:At critical

point:

Event by event fluctuations in heavy ion collisionsEvent by event fluctuations in heavy ion collisions

Hatta and Stephanov, PRL 91 (2003) 102003 Hatta and Stephanov, PRL 91 (2003) 102003

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Susceptibilities at Susceptibilities at > 0 > 0

• Susceptibilities (fluctuation) at q=0 increase rapidly at Tpc

• Second derivatives: Large spike for q near Tpc.

• Susceptibilities (fluctuation) at q=0 increase rapidly at Tpc

• 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:

= 2c2

= 2c2

I

= 2c2

= 2c2

I

= 4!c4

= 4!c4

I

= 4!c4

= 4!c4

I

RG + Clover Wilson

(m/m =0.8, q=0)

RG + Clover Wilson

(m/m =0.8, q=0)

Large enhancement in the fluctuation of baryon number (not in isospin) around Tpc as q increases: Critical point?Large enhancement in the fluctuation of baryon number (not in isospin) around Tpc as q increases: Critical point?

0

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Comparison with Staggered Comparison with Staggered quark resultsquark resultsQuark number (q) and Isospin (I) susceptibilitiesQuark number (q) and Isospin (I) susceptibilities

p4-improved staggered quark , Bielefeld-Swqnsea Collab., Phys. Rev. D71, 054508 (2005)p4-improved staggered quark , Bielefeld-Swqnsea Collab., Phys. Rev. D71, 054508 (2005)

• Similar to the results of Staggered-type quarks• Similar to the results of Staggered-type quarks

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3, Heavy quark free energy and Debye screening mass in QGP medium

Today's poster session by Y. MaezawaToday's poster session by Y. Maezawa

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pcTT

T

TmD )(

Debye screening mass Debye screening mass from Polyakov loop from Polyakov loop correlationcorrelation

),;(1)(

loop-26 SMND Tg

T

Tm f

Leading order thermal perturbation

Leading order thermal perturbation

MeV 2612 fNSM

TT 3~

• Lattice screening mass is not reproduced by LO-type screening mass.

Contribution of NLO-type corrects the LO-type screening mass.

• Lattice screening mass is not reproduced by LO-type screening mass.

Contribution of NLO-type corrects the LO-type screening mass.

LOLO

NLONLO

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SummarySummary We report the current status of our study of QCD thermodynamics lattice simulation with Wilson-type quark action.

We report the current status of our study of QCD thermodynamics lattice simulation with Wilson-type quark action.Critical temperatureCritical temperature

Fluctuation and quark number susceptibility at finite qFluctuation and quark number susceptibility at finite q

Indication of critical point at > 0?Indication of critical point at > 0?

Chiral extrapolation with Nt=4, 6Chiral extrapolation with Nt=4, 6

Heavy quark free energies and Debye mass in QGPHeavy quark free energies and Debye mass in QGP

• LO-type perturbation is not enough to reproduce the lattice Debye mass.• LO-type perturbation is not enough to reproduce the lattice Debye mass.

(Poster session of Y. Maezawa)(Poster session of Y. Maezawa)

Simulation with smaller mass and lattice spacing are in progressSimulation with smaller mass and lattice spacing are in progress

Large enhancement in the fluctuation of baryon number around Tpc as increaseLarge enhancement in the fluctuation of baryon number around Tpc as increase

)6( MeV (3) (4) 176

)4( MeV (5) )4( 180

Nt

NtTc