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RIKEN L unch Seminar. Critical endpoint for deconfinement in matrix model and other effective models. Kouji Kashiwa (Koji Kashiwa). Recent works:. Todays main!. Phys. Rev. D 85 (2012) 114029 , 『 Critical endpoint for deconfinement in matrix and other effective models 』 - PowerPoint PPT Presentation
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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
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!
Polyakov-loop effective potential
Matrix model for deconfinement transition
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
Polyakov-loop effective potential
S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007).
K. Fukushima, Phys. Lett. B 591 (2004) 277.
Polyakov-loop effective potential
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.
…
Formalism Polyakov-loop effective potential
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.
Polyakov-loop effective potential
S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007).
Problem:
K. Fukushima, Phys. Lett. B 591 (2004) 277.
…
Polyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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.
Formalism Polyakov-loop effective potential
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.
Polyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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 !
Polyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
Phys. Rev. D 85 (2012) 114029,『 Critical endpoint for deconfinement in matrix and other effective models 』K.K., R. D. Pisarski, V. V. Skokov.
Matrix model for deconfinement
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.
This work improves these studies:
Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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.
Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
New matrix model for deconfinement transition
SB limit
,Confined vacuum is r = 0Perturbative vacuum is r = 1
,
Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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.
Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
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.
Formalism:Matrix model for deconfinement transitionPolyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge gluon and ghost propagators
Potential from Landau-gauge lattice gluon and ghost propagators
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
Potential from Landau-gauge lattice gluon and ghost propagators
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.
hep-ph/1206.0685,『 Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』K. Fukushima, K.K..
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
Polyakov-loop effective potential
Matrix model for deconfinement
Potential from Landau gauge 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
Matrix model for deconfinement transition
Potential from Landau-gauge lattice gluon and ghost propagators
Numerical results:Matrix model for deconfinement transition
Phys. Rev. D 85 (2012) 114029,『 Critical endpoint for deconfinement in matrix and other effective models 』K.K., R. D. Pisarski, V. V. Skokov.
Matrix model for deconfinement
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.
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.
Numerical results:Matrix model for deconfinement transition
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.
Numerical results:Matrix model for deconfinement transition
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
Numerical results:Gluon and ghost potential in Landau gauge
Potential from Landau-gauge lattice gluon and ghost propagators
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.
hep-ph/1206.0685,『 Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』K. Fukushima, K.K..
Numerical results:Gluon and ghost potential in Landau gauge
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.
Numerical results:Gluon and ghost potential in Landau gauge
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 .
K. Fukushima, K.K., hep-ph/1206.0685.
Numerical results:Gluon and ghost potential in Landau gauge
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.
K. Fukushima, K.K., hep-ph/1206.0685.
Numerical results:Gluon and ghost potential in Landau gauge
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.
K. Fukushima, K.K., hep-ph/1206.0685.
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.