1. Determination of QCD phase diagram from regions with no sign problem Yahiro （ Kyushu University ） Collaborators: Y. Sakai, T. Sasaki and H. Kouno

2. Sign problem of LQCD at finite chemical potential 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 0.4 Prediction of PNJL model When, LQCD is feasible only for the deconfinement phase CEP Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv: 1005.0993[hep-ph](2010). Fermion determinant

3. 1. Purpose and Strategy Purpose is to determine QCD phase diagram at real chemical potential 1.LQCD has the sign problem at real chemical potential 2.Regions with no sign problem I)Imaginary quark-number chemical potential II)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.

4. 2. Imaginary chemical potential Roberge-Weiss Periodicity confined de-confined de- confined de- confined Roberge, Weiss NPB275(1986) RW phase transition

5. QCD partition function where is an element of SU(3) with the boundary condition Z 3 transformation for any integer Z 3 transformation

6. for integer Invariant under the extended Z 3 transformation Extended Z 3 transformation

7. QCD has the extended Z 3 symmetry in addition to the chiral symmetry The Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model Fukushima; PLB591 This is important to construct an effective model. Y. Sakai, K. Kashiwa, H. Kouno and M. Yahiro, Phys. Rev. D77 (2008), 051901; Phys. Rev. D78(2008), 036001. Symmetries of QCD

8. gluon potential quark part (Nambu-Jona-Lasinio type) Polyakov-loop Nambu-Jona-Lasinio (PNJL) model It reproduces the lattice data in the pure gauge limit., Ratti, Weise; PRD75 Fukushima; PLB591 Two-flavor

9. GsGs This model reproduces the lattice data at μ=0., Ratti, Weise; PRD75 Model parameters

10. Phase diagram for deconfinement phase trans. Lattice data: Wu, Luo, Chen, PRD76(07) PNJLRW RW periodicity

11. Chiral RW line Deconfinement Forcrand,Philipsen,NP B642 Phase diagram for chiral phase transition PNJL Chiral Deconfinement

12. 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).

13. Chiral RW line Deconfinement Forcrand,Philipsen,NP B642 Phase diagram for chiral phase transition PNJL Chiral Deconfinement Θ-even higher-order interaction

14. Deconfinement RW Chiral difference ＋ PNJL Forcrand,PhilipsenN PB642 Another correction 8-quark (Θ-even)

15. Vector-type interaction RW Chiral ＋ PNJL ＋ 8-quark (Θ-even)Vector-type (Θ-odd) Deconfinement Forcrand,PhilipsenN PB642

16. Sakai

17. Model building (B) s PNJL extended Z 3 symmetry More precise discussion by K. Kondo, in Hep-th:1005.0314 and His poster. Entanglement interactions such as 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).

18. Phase Diagram by original PNJLPhase Diagram by entanglement- PNJL Entanglement PNJL

19. Isospin chemical potential Entanglement PNJL Real quark-number chemical potential CEP

20. 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.

21. RW E 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. Order of RW phase transition Entanglement PNJL

22. 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).