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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. Sign problem of LQCD at finite chemical potential. Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, arXiv : 1005.0993[ hep -ph](2010).

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Determination of QCD phase diagram from regions with no sign problem

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  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 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

  3. 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.

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

  5. Z3 transformation QCD partition function Z3 transformation where is an element of SU(3) with the boundary condition for any integer

  6. Extended Z3 transformation Invariant under the extended Z3 transformation for integer

  7. 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

  8. 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

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

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

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

  12. 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).

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

  14. Another correction 8-quark (Θ-even) PNJL ＋ RW difference Chiral Forcrand,PhilipsenNPB642 Deconfinement

  15. Vector-type interaction 8-quark (Θ-even) Vector-type (Θ-odd) PNJL ＋ ＋ RW Chiral Forcrand,PhilipsenNPB642 Deconfinement

  16. Sakai

  17. 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.

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

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

  20. 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.

  21. 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

  22. 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).

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