1. Chiral phase transition in magnetic field
毛施君 (Mao Shijun)
西安交通大学(Xi’an Jiaotong University)

2. QCD Phase Diagram HICs： Compact stars：1010~15 Gauss
Early Universe：1024 Gauss
Chiral phase transition
Deconfinement phase transition

3. Lattice QCD Chiral phase transition： Tc(B) is an open question.
refs: G. Bali, et.al, Phys. Rev. D86, (2012);

4. IMC is still an open question.
Magnetic Catalysis (MC) is confirmed by mean field calculation in effective models ---- Dimension Reduction
(Nucl. Phys. B 462, 249 (1996); 563, 361 (1999))
IMC is still an open question.
magnetic inhibition: Fukushima et al., PRL 110, (2013)
contribution from neutral pion
(2) mass gap in large Nc limit:
Toru et al. , PLB 720, 192 (2013)
(3) chirality imbalance:
Huang Mei et al. , PRD 88, (2013)
(4) contribution from sea quark (gluon screening effect):
Bruckmann et al. , JHEP 04, 112 (2013)
(5) weakening of strong coupling:
Pinto et al. , PRC 90, (2014) ……
1. pion properties,
2. feed-down from
pions to quarks

5. NJL model beyond MF SU(2) Nambu--Jona-Lasinio model Idea
NJL模型受BCS理论的启发,被广泛用来研究手征对称性(手征凝聚) (2008, Nobel Prize)。
Idea
(1)Quarks：mean field
(2)Mesons：RPA resummation (quantum fluctuation)
(3)Q-M system：
feed-down from mesons to quarks

6. (1) Gap eq. @ mean field order parameter： chiral condensate
effective quark mass
thermodynamic potential :
quark propagator
in Ritus form:
gap equation:

7. (2) Mesons (quantum fluctuations)
meson Random Phase Approximation
@ Ritus momentum space
pole equation:

8. Pion mass jump @ Mott temperature
pole equation
meson mass jump induced by
dimension reduction of quarks
possible pion enhancement
during the cooling of fireball

9. (3) Gap eq. beyond mean field
mesons
quark-meson system：
meson thermo-
dynamic potential：
meson energy：
transverse velocity：
new gap equation：“running”coupling constant G’(B,T)

10. MC and IMC order parameter low T, m ↑ with B, (MC); G’/G<1,
high T, m ↓ with B, (IMC);
G’/G<1,
meson weakens coupling。
magnetic inhibition

11. chiral phase transition
critical temperature
Tc decreases with B；consistent with LQCD
Inverse Magnetic Catalysis:

12. Summary and outlook quantum fluctuations “running” coupling G’(B,T)
Inverse magnetic catalysis for chiral phase transition
refs：
(1) S.J. Mao, Phys. Lett. B 758, (2016)
(2) S.J. Mao, Phys. Rev. D 94, (2016)
(3) S.J. Mao, Y.X. Wang, PRD accepted,
Outlook: charged meson and condensate;
deconfinement phase transition BMF.

13. Back up

14. G’(B,T)

15. π0 mass and transverse velocity
meson mass：
Goldstone mode
transverse (x,y):
longitudinal (z) :
dimension reduction
Mermin-Wagner-Coleman theorem
possible IMC

16. from IMC to MC critical temperature (2nd), @ μq=0
coexistence quark chemical
potential T=0

17. --- Fu Weijie talk in Yichang

18. chiral and deconfinement phase transition
PNJL

19. Theoretical framework
1. Quark level：solving gap equation with mean field ,mmf
2. Mesons（quantum fluctuations）
3. Feed-down from mesons to quarks：
---- beyond mean field gap eq,mbmf
However,
(1)G is constant;
(3)Running G’(B,T)
From eq(1),
B ↑,m ↑;
G ↑,m ↑;
Mesons

20. meson mass under eB --- MAO, WANG, arXiv:1702.04868 model parameters
Pauli-Villars

21. numerical results
model regularization

22. quark propagator under external magnetic field
---- Ritus propagator
Ritus momentum
refs: Ann. Phys. 69, 555 (1972); Nucl. Phys. B747, 266 (2006);Ann. Phys. 295, 33 (2002) .

23. charged boson propagator (Ritus) under eB
refs: Ann. Phys. 69, 555 (1972);
Nucl. Phys. B747, 266 (2006);
Ann. Phys. 295, 33 (2002) .
polarization functions

24. Lattice QCD Chiral phase transition： Tc(B) is an open question.
refs: G. Bali, et.al, Phys. Rev. D86, (2012);D’Elia et. Al, Phys. Rev. D83, (2011)