Transcript Phase diagram in the imaginary chemical potential reigion

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).
Fermion determinant
Phase factor
In the two-flavor case, the average of the phase factor is
Prediction of PNJL model
e
2 i
Z in the 1+1 system
Z in the 1+1* system
 0 .4
0.4
CEP
When  q  m  / 2 ,
LQCD is feasible only
for the deconfinement phase
1. Purpose and Strategy
Purpose is to determine QCD phase diagram at real chemical
potential
1.
2.
I)
II)
LQCD has the sign problem at real chemical potential
Regions with no sign problem
Imaginary quark-number chemical potential
Real and imaginary isospin chemical potentials
3. Our strategy
1) construct reliable effective models in I)-II)
2) apply the model to real quark-number chemical potential.
2. Imaginary chemical potential
Roberge-Weiss Periodicity
RW
phase
transition
deconfined
de-confined
confined
Roberge, Weiss NPB275(1986)
deconfined
Z3 transformation
QCD partition function
Z ( )  Z (  2  k / 3 )
Z3 transformation
q  Uq ,
A  UAU
1

i
g
 U U 1 ,
where
U ( x , )
is an element of SU(3) with the boundary condition
U ( x ,1 / T )  e
for any integer
k
i 2 k / 3
U ( x ,0 )
Extended Z3 transformation
Z ( )
Invariant under the extended Z3 transformation
q  Uq ,
A  UAU
    2 k / 3
1

i
g
 U U
for integer k
Z ( )  Z (  2  / 3 )
1
,
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
Polyakov-loop Nambu-Jona-Lasinio (PNJL) model
Two-flavor
Fukushima; PLB591
quark part (Nambu-Jona-Lasinio type)
, Ratti, Weise; PRD75
gluon potential
 
1
3
Tr c e
 iA 4 / T
It reproduces the lattice data in
the pure gauge limit.
Model parameters
Gs

d p
3
0
, Ratti, Weise; PRD75
This model reproduces
the lattice data at μ=0.
Phase diagram for deconfinement phase trans.
PNJL
RW
RW periodicity
Lattice data:
Wu, Luo, Chen, PRD76(07)
Phase diagram for chiral phase transition
PNJL
RW line
Chiral
Deconfinement
Forcrand,Philipsen,NP
B642
Chiral
Deconfinement
Model building
A. 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).
Phase diagram for chiral phase transition
PNJL
RW line
Chiral
Deconfinement
Forcrand,Philipsen,NP
B642
Chiral
Deconfinement
Θ-even higher-order interaction
Another correction
8-quark (Θ-even)
PNJL
＋
RW
difference
Chiral
Forcrand,PhilipsenN
PB642
Deconfinement
Vector-type interaction
8-quark (Θ-even)
PNJL
Vector-type (Θ-odd)
＋
＋
RW
Chiral
Forcrand,PhilipsenN
PB642
Deconfinement
Sakai
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 G s (  )
PNJL
s
Gs
extended Z3 symmetry
A0 
a3
A0 
a8
a
a
 A0 
a3
 A0 
a8
a
 i
  Tr e

a
 a0
a3
 a0
a8
a
a
A0   i  A0 
3
3
8
8


More precise discussion
by K. Kondo,
in Hep-th:1005.0314
and His poster.
2
Entanglement PNJL
Phase Diagram by original PNJL
Phase Diagram by entanglement- PNJL
Entanglement PNJL
Isospin chemical potential
Real quark-number chemical potential
CEP
Summary
1) 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.
Order of RW phase transition
RW
M. D’Elia and F. Sanfilippo, Phys. Rev. D 80, 11501 (2009).
P. de Forcrand and O. Philipsen, arXiv:1004.3144 [heplat](
2010).
E
The order is
first order for small and large quark masses, but
second order for intermediate masses.
Entanglement PNJL
List of papers
1. Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro.
Phys. Rev. D77 (2008), 051901.
2. Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro.
Phys. Rev. D78(2008), 036001.
3. 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).