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Chiral Critical Surface in the NJL model

Hiroaki Kohyama

(幸山 浩章)

Academia Sinica / NCTS National Taiwan University

2010.04.30 Fri 14:20

(2)

Contents

1. Introduction

1.1 QCD phase diagram 1.2 Chiral vs Confinement 1.3 Chiral Critical Surface

2. NJL model

3. Our recent work 4. future works

(3)

1. Introduction

(4)

QCD phase diagram

Quark Chemical Potential

Temperature

Quark-Gluon Plasma

Hadron Color Super

CFL

(5)

Quark Chemical Potential

Temperature

QGP

Hadron CS

QCD phase diagram

Heavy Ion C.

Lattice QCD

Model Studies Neutron Star

(6)

Quark Chemical Potential

Temperature

Asymptotic free

Quark Confined

QCD phase diagram

Exp.

Lattice

(7)

Quark Chemical Potential

Temperature

Asymptotic free

Quark Confined

QCD phase diagram

Exp.

Lattice

Nothing concrete!

We have to rely on some effective model

(8)

Chiral vs Confinement?

(9)

Chiral vs Confinement?

: for deconfinement phase transition : for chiral phase transition

(’t Hooft & Casher)

A. Casher, PLB 83 (1979) 395.

G. ’t Hooft, et al, some book, NY (1980).

Critical temperature at Critical Point

Although it is not proven, but

(10)

Chiral phase diagram

O.K., let’s study chiral phase transition.

Quark Chemical Potential

Temperature

Chiral restored

Chiral broken

(11)

Chiral Critical Surface

(12)

Critical Surface?

We treat current quark masses as parameters.

Idea:

Quark Chemical Potential

Temperature

(13)

Chiral Critical Surface

P. de Forcrand & O. Philipsen, arXiv:0811.3858.

T

CP

1st Crossover

µ µ

Crossover

T

Text

(14)

Columbia Plot

airXiv:hep-ph/0303042 (review)

(15)

2. Nambu Jona-Lasinio

(16)

NJL Lagrangian

Lagrangian:

What the relation between QCD?

Natural question:

(17)

QCD & NJL

4-point interaction may come from

(18)

Contact interaction

(19)

NJL model

Parameters are fixed by

(20)

Gap equation

Effective potential:

where

(21)

Solutions of Gap eq.

0 100 200 300 400 500 600

0 50 100 150 200 250 300 350

Constituent Quark Masses[MeV]

Temperature[MeV]

Mu Ms

0 100 200 300 400 500 600

0 100 200 300 400 500 600

Constituent quark masses[MeV]

Chemical potential µ[MeV]

Mu Ms

Crossover 1st

(22)

Phase diagram in NJL

0 50 100 150 200 250

0 100 200 300 400 500

Temperature [MeV]

Quark Chemical Potential [MeV]

Critical Point

Chiral broken

Chiral restored

Crossover

1st

(23)

Critical behavior

0 2 4 6 8 10 12 14

0 0.5 1 1.5 2 2.5 3

Strange Quark Mass[MeV]

Light Quark Mass[MeV]

Columbia Plot Critical Surface

1st

Crossover

0 1

2 3 4

5 0

5 10 15 20 25 0

50 100 150 200 250 300

Chemical potential[MeV]

Light Quark Mass [MeV]

Strange Quark Mass [MeV]

(24)

3. Our recent work

based on

J.-W. Chen, K. Fukushima, H. K., K. Ohnishi, U. Raha, PRD 81, 071501(R) (2010)

(25)

Motivation

0 20 40 60 80 100 120 140

0 5 10 15 20 25 30 35

Strange Quark Mass[MeV]

Light Quark Mass[MeV]

LQCD phys. point

NJL

Huge difference! WHY?

(26)

Lattice, too coarse?

Phillipsen, arXiv:0910.0785 Endrodi, et al, arXiv:0710.0998

Lattice discretization Nt may be crucial.

(27)

Lattice discretization

Time d. : Nt = 4 Space d. : Ns = 32

seemingly too coarse

Ns Nt

(28)

Check in NJL

Space direction is OK, let’s leave it intact.

Time d. : Nt = 4 problematically small Space d. : Ns = 32 decent

Time direction may be trouble, so we will try

Strategy:

the finite frequency summation.

We shall modify the model cut-off.

(29)

Modified NJL

Finite temperature field theory:

Let’s change summation,

leading smaller cut-off (larger ).

This mimics Lattice situation.

(30)

Parameter fit

Fit the parameters by

Larger N means smaller

Running coupling constant

(31)

Results

(32)

Comparison

Nt=4

(33)

Conclusion

Lattice discretization is too coarse!

(34)

4. future works

(35)

Generalize to finite mu

0 50 100 150 200 250

0 100 200 300 400

Temperature [MeV]

Quark Chemical Potential [MeV]

Critical Point

N=!

N=50 N=15

(36)

Critical Surface

0 1

2 3

4 5 0

5 10 15

20 25 0

50 100 150 200 250 300

Chemical potential[MeV]

Light Quark Mass [MeV]

Strange Quark Mass [MeV] 0 1

2 3 4 5 0

5 10

15 20

25 0

50 100 150 200 250 300

Chemical potential[MeV]

Light Quark Mass [MeV]

Strange Quark Mass [MeV]

N=15 N=∞

(37)

Summary

Tested the temporal UV-cutoff effect

explains the difference LQCD & NJL

(38)

Ask for ...

Confinement & Chiral transition

Maybe from some correspondence

Sign Problem in Lattice (maybe Dr.Takimi can)

Finite chemical potential region

Something new from condensed matter p. ? Effective model from first principle?

Mathematical aspects

Confining order parameter by string?

(39)

謝謝大家

參考文獻

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