determination of qcd phase diagram from regions with no sign problem n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Determination of QCD phase diagram from regions with no sign problem PowerPoint Presentation
Download Presentation
Determination of QCD phase diagram from regions with no sign problem

Loading in 2 Seconds...

play fullscreen
1 / 22

Determination of QCD phase diagram from regions with no sign problem - PowerPoint PPT Presentation


  • 82 Views
  • Uploaded on

Determination of QCD phase diagram from regions with no sign problem. Yahiro ( Kyushu University ). Collaborators: Y. Sakai, T. Sasaki and H. Kouno. Sign problem of LQCD at finite chemical potential. Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv : 1005.0993[ hep -ph](2010).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Determination of QCD phase diagram from regions with no sign problem' - kylene


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
determination of qcd phase diagram from regions with no sign problem

Determination of QCD phase diagram from regions with no sign problem

Yahiro

(Kyushu University)

Collaborators:

Y. Sakai, T. Sasaki and H. Kouno

slide2

Sign problemof LQCD at finite chemical potential

Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv: 1005.0993[hep-ph](2010).

Fermion determinant

Phase factor

In the two-flavor case, the average of the phase factor is

Z in the 1+1 system

Z in the 1+1* system

Prediction of PNJL model

0.4

CEP

When ,

LQCD is feasible only

for the deconfinement phase

1 purpose and strategy
1. Purpose and Strategy

Purpose is to determine QCD phase diagram at real chemical potential

LQCD has the sign problem at real chemical potential

Regions with no sign problem

Imaginary quark-number chemical potential

Real and imaginary isospinchemical potentials

3. Our strategy

1) construct reliable effective models in I)-II)

2) apply the model to realquark-numberchemical potential.

2 imaginary chemical potential
2. Imaginary chemical potential

Roberge-Weiss Periodicity

Roberge, Weiss NPB275(1986)

de-

confined

de-confined

de-

confined

RW

phase

transition

confined

slide5

Z3 transformation

QCD partition function

Z3 transformation

where

is an element of SU(3) with the boundary condition

for any integer

slide6

Extended Z3 transformation

Invariant under the extended Z3 transformation

for integer

slide7

Symmetries of QCD

Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro,

Phys. Rev. D77 (2008), 051901; Phys. Rev. D78(2008), 036001.

QCD has the extended Z3 symmetry

in addition to the chiral symmetry

This is important to construct an effective model.

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

Fukushima; PLB591

slide8

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

Two-flavor

Fukushima; PLB591

gluon potential

quark part (Nambu-Jona-Lasinio type)

It reproduces the lattice data in the pure gauge limit.

, Ratti, Weise; PRD75

slide9

Model parameters

Gs

This model reproduces the lattice data at μ=0.

, Ratti, Weise; PRD75

slide10

Phase diagram for deconfinement phase trans.

PNJL

RW

Lattice data:

Wu, Luo, Chen, PRD76(07)

RW periodicity

slide11

Phase diagram for chiral phase transition

PNJL

RWline

Chiral

Deconfinement

Forcrand,Philipsen,NP B642

Chiral

Deconfinement

slide12

Model building

PNJL with higher-order interactions

Y. Sakai, K. Kashiwa, H. Kouno, M. Matsuzaki, and M. Yahiro,

Phys. Rev. D 79, 096001 (2009).

B. PNJL with an effective four-quark vertex

depending on Polyakov loop

Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro,

arXiv:1006.3648[Hep-ph](2010).

slide13

Phase diagram for chiral phase transition

PNJL

RWline

Chiral

Deconfinement

Forcrand,Philipsen,NP B642

Chiral

Deconfinement

Θ-even higher-order interaction

slide14

Another correction

8-quark (Θ-even)

PNJL

RW

difference

Chiral

Forcrand,PhilipsenNPB642

Deconfinement

slide15

Vector-type interaction

8-quark (Θ-even)

Vector-type (Θ-odd)

PNJL

RW

Chiral

Forcrand,PhilipsenNPB642

Deconfinement

slide17

Model building (B)

B. PNJL with an effective four-quark vertex depending on Polyakov loop

Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv:1006.3648[Hep-ph](2010).

Entanglement interactions such as

PNJL

s

extended Z3 symmetry

More precise discussion

by K. Kondo,

in Hep-th:1005.0314

and His poster.

slide18

Entanglement PNJL

Phase Diagram by original PNJL

Phase Diagram by entanglement- PNJL

slide19

Entanglement PNJL

Isospin chemical potential

Real quark-number chemical potential

CEP

summary
Summary
  • We proposed two types of PNJL models.

One has higher-order interactions and the other has an entanglement vertex.

2) Both the models give the same quality of agreement with LQCD data.

3) In both the models, CEP can survive.

Last question: Which model is better ?

PNJL with the entanglement vertex is more reliable.

slide21

Order of RW phase transition

M. D’Elia and F. Sanfilippo, Phys. Rev. D 80, 11501 (2009).

P. de Forcrand and O. Philipsen, arXiv:1004.3144 [heplat](

2010).

The order is

first order for small and large quark masses, but second order for intermediate masses.

RW

Entanglement PNJL

E

list of papers
List of papers

1. Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro.

Phys. Rev. D77 (2008), 051901.

Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro.

Phys. Rev. D78(2008), 036001.

Y. Sakai, K. Kashiwa, H. Kouno, M. Matsuzaki and M. Yahiro.

Phys. Rev. D78(2008), 076007.

4. Y. Sakai, K. Kashiwa, H. Kouno, M. Matsuzaki, and M. Yahiro,

Phys. Rev. D 79, 096001 (2009).

5. Y. Sakai, H. Kouno, and M. Yahiro, arXiv: 0908.3088(2009).

6. T. Sasaki, Y. Sakai, H. Kouno, and M. Yahiro, arXiv:hepph/

1005.0910 [hep-ph] (2010).

7. Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv: 1005.0993

[hep-ph](2010).

8. Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv:1006.3648

[Hep-ph](2010).