Chiral phase transition in magnetic field

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Presentation transcript:

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

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

Lattice QCD Chiral phase transition： Tc(B) is an open question. refs: G. Bali, et.al, Phys. Rev. D86, 071502 (2012);

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, 031601 (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, 054009 (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, 025203 (2014) …… 1. pion properties, 2. feed-down from pions to quarks

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

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

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

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

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

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

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

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, 195-199 (2016) (2) S.J. Mao, Phys. Rev. D 94, 036007 (2016) (3) S.J. Mao, Y.X. Wang, PRD accepted, 1702.04868 Outlook: charged meson and condensate; deconfinement phase transition BMF.

Back up

G’(B,T)

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

from IMC to MC critical temperature (2nd), @ μq=0 coexistence quark chemical potential (1st), @ T=0

--- Fu Weijie talk in Yichang

chiral and deconfinement phase transition PNJL

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

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

numerical results model parameters @Pauli-Villars regularization

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) .

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

Lattice QCD Chiral phase transition： Tc(B) is an open question. refs: G. Bali, et.al, Phys. Rev. D86, 071502 (2012);D’Elia et. Al, Phys. Rev. D83, 114028(2011)