第十 届 QCD 相变与相对论重离子 物理研讨会 , August 8-10 2 0 1 3

1. 第十届QCD相变与相对论重离子物理研讨会, August 8-102013 • Role of vector interactions and the induced non-anomaly flavor-mixing at finite isospindensity • 张 昭 • 华北电力大学（北京）（NCEPU） • OUTLINE • Introduction • No-anomaly flavor-mixing induced by vector interactions • Two critical points at finite • for weak anomaly flavor-mixing? • Equivalence for QCD phase transition at finite 𝛍 and ? • Summary

2. 1. 1QCD critical point • Chiral restoration (m=0) well defined • Order parameter: Chiral condensate • Two-flavor with the U(1)A anomaly 2nd-orderphase transition with O(4)universality class Pisarski and welczek, PRD 29, 338(1984) Critical point for m>0 ? It’s Location? Only one ? It’s number ? How to detect it in HIC Expt. ?

3. 1.2. Conjectured phase diagram of QCD 1 2. 3. K. Fukushima & T. Hatsuda Common feature: At least one QCD critical point included. Its existence and location is dynamical problem, determined by QCD itself Problem: Nonperturbative The first principle at finite density, sign problem QCD models and QCD-like theory

4. 1.3. Critical point structure from NJL model: one or zero 2-flavor NJL C. Sasaki, B. Friman, and K.Redlich, PRD75, 054026 (2007) 2+1 flavor PNJL N. Bratovic, T. Hstsuda, and W. Weise, PLB 719 (2003)131

5. 1.4. Multiple critical points in NJL model with CSC M. Kitazawa, T. Koide, Y. Nemoto and T.Kunihiro, PTP (’022) Abuki, Baym, Hatsuda and Yamamoto, PRD 81 (2010) 125010 Denied by H. Basler and M. Buballa in PRD 82 (2010) 094004 Vector interaction Axial anomaly Vector interaction + Charge neutrality Charge neutrality + Axial anomaly Z. Z., K. Fukushima, T.Kunihiro, PRD79 (2009) 014004 Z. Z., and T. Kunihiro, PRD80(2009)014015; PRD83 (2011)

6. 1.5Two critical points at finite isospin chemical potential Two critical points at finite ? Random Matrix Model NJL Model ( without flavor-mixing ) ( without flavor-mixing ) B. Klein, D. Toulblan and J.J.M. Verbaarschot, PRD 68 (2003) 014009 D. Toulblanand J.B. Kogut, PLB 564 (2003) 212

7. 1.6 The effect of Axial anomaly-mixing Effect of the flavor-mixing induced by axial anomaly Two-flavor NJL model M. Frank, M. Buballa and M. Oertel , PLB 562 (2003) 221 Mass flavor-mixing ‘t Hooft interaction Rough estimate: Two first-order lines for The fate of the two critical points depends on the degree of the U(1)A asymmetry !

8. 1.6 U(1)A restoration at finite T in lattice simulations The axial anomaly effect may be suppressed significantly near the chiral boundary ? ! Recent lattice formulations on the U(1)A symmetry restoration at finite T (1) Chiral symmetry restoration U(1)A symmetry restoration Dirac spectral density Lattice: Domain wall fermions Bazavov, et al. (HotQCD Collaboration) PRD 86, 094503 (2012) Banks-Casher relation

9. 1.7 U(1)A restoration at finite T in lattice simulations Recent lattice formulations on the U(1)A symmetry restoration at finite T (2) Dirac Spectral density Lattice: Overlap fermions G. Cossu, S. Aoki et al. PRD 87, 114514 (2013)

10. 2. Non-anomaly flavor-mixing induced by vector interactions Both Lattice results suggest the axial U(1)A symmetry is effectively restored in the Chiral symmetric phase (for T>=Tc). If it is true, we can expect that the same thing may happen at finite density. The question: Can the two critical points at finite isospin chemical potential survive if the anomaly flavor-mixing is suppressed significantly near the chiral boundary ? Other possible flavor-mixing ? One possibility : Mismatched vector interactions in the isoscalar and Isovector channels may lead to a non-anomaly flavor mixing at finite Isospin chemical potential.

11. 2. Non-anomaly flavor-mixing induced by vector interactions Two types of vector interactions in NJL type model: Vector-isoscalar interaction Vector-isovector interaction General four-fermion interactions with the flavor symmetry Chiral symmetry does not require the two couplings are identical in the four-fermion interaction model

12. 2. Non-anomaly flavor-mixing induced by vector interactions The argument for the mismatched vector interactions by C. Sasaki et al. L. Ferroni and V. Koch, PRC 83,045205(2011) C. Sasaki, B. Friman, and K.Redlich, PRD75, 054026 (2007) Very important for the determination of the off-diagonal susceptibility

13. 2. Non-anomaly flavor-mixing induced by vector interactions The most popular version of NJL model: At the mean filed level, usually only Hartree contribution is considered Including the Fock term: >0 One gluon exchange

14. 2. Non-anomaly flavor-mixing induced by vector interactions Constrait from the chiral curvatures at finite 𝛍 and Curvature: Recent lattice calculation: Paolo Cea et al. PRD 85,094512 (2012) Extending the idea to finite < 0 ! Near Tc for zero 𝛍 N. Bratovic, T. Hstsuda, and W. Weise, PLB 719 (2003)131

15. 2. Non-anomaly flavor-mixing induced by vector interactions Our lagrangian : Baryon and Isospin chemical potentials: Effective quark chemical potentials are shifted by vector interactions Non-anomaly Flavor-mixing Isospin asymmetry is weakened

16. 2. Non-anomaly flavor-mixing induced by vector interactions Mass flavor-mixing due to the ‘t Hooft interaction Thermal potential at the mean field level Two types of flavor-mixing !

17. 3. Phase diagrams at finite with the vector interactions Phase diagrams at small isospin chemical potentials under the influence of the non-anomaly flavor-mixing (without the anomaly flavor-mixing ) must be much stronger than To change the two 1st order lines into one ,

18. 3. Phase diagrams at finite with the vector interactions Phase diagrams at finite isospin chemical potential under the influence of vector interactions and the weak anomaly flavor-mixing .

19. 3. Phase diagrams at finite with the vector interactions Phase diagram at finite isospin chemical potential under the influence of vector interactions and the weak anomaly flavor-mixing .

20. 3. Phase diagrams at finite with the vector interactions vs Our results M. Frank, M. Buballa and M. Oertel , PLB 562 (2003) 221

21. 3. Phase diagrams at finite with the vector interactions

22. 4. Equivalence of QCD phase transition at finite 𝛍 and ? The boundary can Be determined by Lattice QCD at based on the QCD inequalities and the large-Ncorbifold equivalence For Nc=3 ? The mean field calculations based on QCD models, such as (P)NJL, (P)QM and RMM etc., support such a conclusion.

23. 4. Equivalence of QCD phase transition at finite 𝛍 and ? Mean field level M. Hanada, Y. Matruo, and N. Yamamoto, PRD 86, 074510 (2012) In our case, ≠ (if the mismatched vector interactions are included )

24. 5. Summary and outlook • Mismatched vector interactions can lead to a non-anomaly flavor-mixing • The two critical points at small isospin chemical potential can be ruled out if is much stronger than • For weak anomaly flavor-mixing, the two separate 1st order transition due to the isospin asymmetry can be changed into one by vector interactions, where > is not required ( the physical • case ? ) • Chiral transition equivalence at finite 𝛍 and may be violated obviously if the vector interaction difference is large. • U(1)A symmetry restoration at finite T should be further studied • In lattice formulation • Lattice study on the U(1)A symmetry restoration at finite isospin chemical potential?