Critical endpoint for deconfinement in matrix model and other effective models

Critical endpoint for deconfinement in matrix model and other effective models

Kouji Kashiwa (Koji Kashiwa)Recent works:

Phys. Rev. D 85 (2012) 114029,『 Critical endpoint for deconfinement in matrix and other effective models 』K.K., R. D. Pisarski, V. V. Skokov.

In preparation ( will be submitted soon ),『 Extraction of nontrivial correlation between chiral and deconfinement transitions from two-color QCD at imaginary chemical potential 』K.K., T. Sasaki, H. Kouno, M. Yahiro.

hep-ph/1206.0685,『 Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』K. Fukushima, K.K..

RIKEN Lunch Seminar

Todays main!

Todays sub-main

In preparation,『 Mesonic fluctuation effects on Roberge-Weiss endpoint』K.K..

Introduction

Schematic figure of QCD phase diagram

3-d Colombia plot

Chiral and deconfinement transition

Formalism

Matrix model for deconfinement transition

Polyakov-loop effective potential

Potential from Landau-gauge lattice propagators

Numerical results and discussion

Summary

Contents:

Introduction:QCD phase diagram

At m=0, lattice QCD simulations provide important information.

At finite m, lattice QCD simulations are broken down…

Effective model approaches are widely used.

K. Fukushima and T. Hatsuda, Rept.Prog.Phys.74 (2011) 014001.Schematic QCD phase diagram

Deconfinement phase transition

Chiral phase transition Chiral condensate

Polyakov-loop

It generate the heavy constituent quark mass at low temperature and baryon density.

Order-parameter of the spontaneous chiral symmetry breaking. 0

0

Free energy for single quark excitation.

0M m Spontaneous mass generation

0 　/~ F Te 1 0F

F

L. D. McLerran and B. Svetitsky, Phys. Rev. D 24 (1981) 450.

Order-parameter of the spontaneous center symmetry breaking.

F, , T Vm

qq

1 Tr c

LN

(simple case)

(at least in the infinite quark mass limit)

Introduction:Chiral and deconfinement transition

Introduction:Colombia plot

C. Bonati, P. de Forcrand, M. D'Elia, O. Philipsen, F. Sanfilippo, arXiv:hep-ph/ 1201.2769.

3-d Clombia plotex.) H. Saito, et al, (WHOT-QCD Collaboration), arXiv:1202.6113.

ex.) P. de Forcrand, O. Philipsen, arXiv:hep-lat/1004.3144.

ex.) M. D'Elia, F. Sanfilippo, PRD 80 (2009) 111501(R).

Introduction:Colombia plot

To understand the QCD phase structure, different type of the chemical potential may be important!

Recently, several situations are energetically considered.

Imaginary chemical potential

Iso-spin chemical potential with zero baryon chemical potential or finite imaginary m.

Flavor-dependent twisted boundary angle

P. Cea, L. Cosmai, M. D'Elia, A. Papa, PoS LAT2009:192,2009.Y. Sakai, H. Kouno, M. Yahiro, J. Phys. G 37 (2010) 105007.

H. Kouno, Y. Sakai, T. Makiyama, K. Tokunaga, T. Sasaki, M. Yahiro, arXiv:hep-ph/1202.5584.

So many works…

Response of temporal boundary angle for quarks (Dual quark condensate)

E. Bilgici, F. Bruckmann, C. Gattringer, C. Hagen, Phys. Rev. D 77 (2008)094007.C. S. Fischer, Phys. Rev. Lett. 103 (2009) 052003.

K. K., H. Kouno, M. Yahiro, Phys. Rev. D 80 (2009) 117901.

(Such situations are sometime not realistic, but it is very important!)

Introduction:Polyakov-loop dynamics

Most simple method to investigate the chiral and deconfinement transition:

Polyakov-loop extended Nambu—Jona-Lasinio (PNJL) model

Polyakov-loop extended quark-meson (PQM) model

Both models are consistent at least in the first-order derivative expansion.T. Eguchi, Phys. Rev. D14 (1976) 2755.

The most important problem is how to describe the deconfinement transition.

The gluon dynamics is introduced by additional terms in addition to the matter part.

We need the effective potential to describe the Polyakov-loop dynamics!



Potential from Landau-gauge lattice gluon and ghost propagators

Formalism

Formalism Polyakov-loop effective potential

Polyakov-loop effective potential are based on the strong coupling expansion


S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007).

K. Fukushima, Phys. Lett. B 591 (2004) 277.


Matrix model for deconfinement

Potential from Landau gauge gluon and ghost propagators

Logarithm term comes from the Haar measure. (Vandermond determinant)

Parameters are fitted to reproduce LQCD data in pure gauge limit.

…


Polyakov-loop effective potential are based on the strong coupling expansion

We can not go large Nc easily.

Transverse gluon effects are still bit unclear.


S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007).

Problem:

K. Fukushima, Phys. Lett. B 591 (2004) 277.

…




Recently, more systematic studies not this approach is done.

Above potential is the limiting case of their potential.

C. Sasaki and K. Redlich, hep-ph/1204.4330.M. Ruggieri and , hep-ph/1204.5995.


Moreover, the potential can not be expressed by the Polyakov-loop and its conjugate in the case of the color number larger than four.

Polyakov-loop is expressed by the fundamental trace, but this one-loop potentials have the adjoint trace.

The perturbative potential at high T

In following, I call it as Yaffe potential.




N. Weiss, Phys. Rev. D 24 (1981) 475.

D. Gross, R. D. Pisarski, and L. Yaffe, Rev. Mod. Phys. 53 (1981) 43.

M. Sakamoto, K. Takenaga. Phys. Rev. D 76 (2007) 085016.

N. Weiss, Phys. Rev. D 24 (1981) 475.

For example, see P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009.

This potential leads the perturbative vacuum.

Formalism:Matrix model for deconfinement transition

The Polyakov-loop effective potential approach has some big problems.

The natural approach is based on the perturbative potential to satisfy the clear Stefan-Boltzmann limit and have the connection with large Nc.

This approach is based on the Weiss potential.

Effects of transverse gluon are clear.

There is unclearness how to include the non-perturbative effect…

( In this study, we add additional one-loop potential with few parameter. )

To describe the deconfinement transition, we must introduce the non-perturbative effects.

Matrix model for deconfinement transition !




P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009.A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, PRD 83 (2011) 034022.

Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential






This work improves these studies:




Polyakov-loop dynamics is dominated by the gluon one-loop potential

It comes from the adjoint trace.

SB limit+

Basic matrix model for deconfinement

Longitudinal gluon contribution is vanished by the Fadeev-Popov determinant.

This potential comes from transverse gluon.

Non-perturbative effects are taken into account by the one-loop order.

There is the cubic term which can lead the first-order transition.

A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, Phys. Rev. D 83 (2011) 034022.




New matrix model for deconfinement transition

SB limit

,Confined vacuum is r = 0Perturbative vacuum is r = 1

,




Modification of parameter

Meisinger-Miller-Ogilvie model

It is equivalent with the MIT Bag constant.

A. Dumitru, Y. Guo, Y. Hidaka, C. P. Korthals Altes, R. D. Pisarski, arXiv:hep-ph/1205.0137.




Fermion dynamics

Asymptotic behavior (x to infinity)of the second kind of

the modified Bessel function

f

Large quark mass expansion

Boltzmann factor

Some details at high T; P. N. Meisinger, M. C. Ogilvie, Phys. Rev. D 65 (2002) 056013.





We construct the effective model which based on the perturbative one-loop potential.

To obtain better result, we newly introduce the one more parameter and r2 coefficient.

We can describe all T region.

New parameter make the interaction measure more consistent with lattice QCD data.

r2 coefficient remove the unphysical behavior below Tc.

There are other methods to include the non-perturbative effects.

Numerical results:Gluon and ghost potential in Landau gauge


This study is a extension to finite T of the paperJ. Braun, H. Gies, J. M. Pawlowski , Phys. Lett. B 684 (2010) 262

by using more simple approach.

They based on the FRG and DS equation.


Introduction:Gluon and ghost potential in Landau gauge

We start from the Landau-gauge gluon and ghost propagators obtained by lattice QCD simulation.

The non-perturbative effect came into through the infrared and mid-momentum region of propagators.

Main uncleanness come from error of lattice QCD data, for example the finite size effect.

Transverse gluon and ghost propagators




In the matrix model for deconfinement, the non-perturbative effects are taken in to accountby the additional one-loop potential.

Zc

Lattice data: R. Aouane et al., PRD 85 (2012) 034501.

Numerical results



Numerical results:Matrix model for deconfinement transition




This work improves these studies:

Model dependenceis quite large!

It is reflected how strong the first-order is

in heavy quark mass limit.

The quark mass is then considered as

the external field which breaksthe Z3 symmetry explicitely.

2-d Clombia plotK.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029.


Model dependenceis quite large!

It is reflected how strong the first-order is

in heavy quark mass limit.

The quark mass is then considered as

the external field which breaksthe Z3 symmetry explicitely.

2-d Clombia plotK.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029.


We can observe two-peak structure?

The dynamical quark should be introduced.

Non-trivial structure appears!

At this quark mass, previous approximated expression is already good.

However, such simple term leads thisnontrivial structure!

Interaction measure

T [GeV]

K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029.Numerical results:Matrix model for deconfinement transition

Interaction measure

Model difference also appearson the interaction measure.

Log-type Polyakov-loop effective potentialdose not have the two-peak structure.

K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029.Numerical results:Matrix model for deconfinement transition



This study is a extension to finite T of the paperJ. Braun, H. Gies, J. M. Pawlowski , Phys. Lett. B 684 (2010) 262

by using more simple approach.

They based on the FRG and DS equation.



Gluon propagator Ghost dressing function

Propagators in Landau gauge We use Gribov-Stingl type function to fit LQCD data.

Lattice data: R. Aouane et al., PRD 85 (2012) 034501.

T = 0.86 Tc T = 0.84 Tc

K. Fukushima, K.K., hep-ph/1206.0685.


Phase transition in SU(2) and SU(3)

We can naturally reproduce the first and second order deconfinement transition!

Tc = 286 MeV for SU(3)

We use the same values shown inR. Aouane et al., PRD 85 (2012) 034501 .



Thermodynamics

Near Tc, we obtain consistent result with lattice QCD data.

Lattice data: S. Datta and S. Gupta, PRD 82 (2010) 114505.

At low T, energy and entropy densities go to minus…

Ghost effects are still bit strong…

In this study,we neglect the temperature- dependence of propagators.

SB limit can be obtained.



Quark contributions

We introduce the NJL model as a mimic of matter part of QCD.

LQCD data: S. Borsanyi, et al., arXiv:hep-lat/1005.3508.

NJL part:

LQCD data: S. Borsanyi, et al., JHEP 11 (2010) 077.


Summary

Summary:

We investigate the deconfinement transition by using matrix model which is based on the perturbative one-loop potential.

In the upper part of the Colombia plot, we can see the large difference between effective models.

There are several method to include the non-pertubative effects to describe the deconfinement transition:

Additional one-loop potentials with one or two parameter,

Landau-gauge lattice gluon and ghost propagators,

These models can reproduce the correct form of perturbative behavior of QCD and therefore,it may suitable to investigate the QCD phase structure

than the standard Polyakov-loop effective potential.

Critical endpoint for deconfinement in matrix model and other effective models

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