1. Lang Yu Institute of High Energy Physics, CAS collaboration with Hao Liu, Mei Huang Induced local CP violation in chiral symmetric phase and inverse magnetic catalysis

2. Outline Introduction Model in the SU(2) f Case Model in the SU(3)f Case Summary and Outlook

3. Introduction

4. Strong Magnetic Fields in QCD

5. B B CME CVE Vacuum superconductor Inverse Magnetic Catalysis Magnetar (Inverse) Magnetic Catalysis QCD Phase Diagram under Magnetic Fields

6. Magnetic Catalysis

7. Overview of Previous Calculations

8. T c vs. eB

9. Recent lattice QCD results (Bali et al., JHEP 1202, 044, 2012) Motivation and Inverse Magnetic Catalysis

10. Possible Mechanisms to the Problem Kenji Fukushima and Yoshimasa Hidaka (2012): Contributions from neutral pions F. Bruckmann, G. Endrodi and T. G. Kovacs (2013): Contributions from sea quarks Jingyi Chao, Pengcheng Chu and Mei Huang (2013): Local chirality imbalance induced by sphaleron transition M. Ferreira, P. Costa, O. Lourenço, T. Frederico, C. Providência (2014): Running coupling constant under magnetic fields

11. Local CP Violation and Chirality Imbalance The nontrivial topological gluon configuration is determined by the topological charge: The chirality imbalance is induced by the nonzero topological charge through the axial anomaly of QCD

12. Local chirality imbalance Chirality imbalance destroys chiral condensate Why chirality imbalance destroys chiral condensate?

13. Local CP Violation and Chirality Imbalance Thermal effect Enhanced by B Q T =0 ~Tc~Tc -Q T +Q T B↑

14. Model in the SU(2) f Case

15. NJL Model with the Axial-vector Interaction The Lagrangian density: The mean field approach:

16. Instanton–anti-instanton Molecule Model T. Schafer, E. V. Shuryak and J. J. M. Verbaarschot(1995): The instanton–anti-instanton molecule pairs are dominant for The molecule-induced effective four-quark interactions give G A <0

17. Formalism Find the thermodynamical potential The saddle point equations

18. Numerical Results At eB=0 for different r A = G A /G S

19. Numerical Results The competition between chiral condensate and local chirality imbalance low T high T Ω

20. Numerical Results For r A =−0.75 and r A =−0.85 at eB=0, 0.2, 0.5, 0.8 GeV 2 r A =−0.75r A =−0.85

21. Numerical Results The critical temperatures T c and T 5c

22. Model in the SU(3) f Case

24. LY, Jos van Doorsselaere, Mei Huang, arXiv:1410.xxxx Iso-scalar axial-vector channel

25. LY, Jos van Doorsselaere, Mei Huang, arXiv:1410.xxxx Iso-scalar axial-vector channel for u, d r A =−0.5

26. LY, Jos van Doorsselaere, Mei Huang, arXiv:1410.xxxx Iso-scalar axial-vector channel for u, d, s r A =−0.5

27. For Light Quark Condensates

28. For Strange Quark Condensate

29. Summary and Outlook Spontaneous generation of local CP violation and chirality imbalance in the chiral symmetric phase External magnetic fields lower the critical temperature for the local CP-odd phase transition and catalyze the chirality imbalance Other mechanisms ? Finite chemical potential ?

30. Thank You for Your Attention !