Abstract
We systematically study quantum effect on chiral and $U_A(1)$ symmetry breaking under external electromagnetic fields in the frame of equal-time Wigner function formalism. We derive the transport and constraint equations for the quark distribution functions and the chiral and pion condensates in a Nambu--Jona-Lasinio model. By taking semi-classical expansion of the equations, chiral symmetry is broken at classical level, while $U_A(1)$ symmetry breaking happens only at quantum level. Beyond quasi-particle approximation, the quark off-shell effect leads to strong oscillation for the chiral and pion condensates.
Highlights
In the chiral limit with zero current quark mass, the Lagrangian density of the quantum chromodynamics (QCD) respects the symmetry of ULð3Þ × URð3Þ 1⁄4 UVð1Þ× UAð1Þ × SULð3Þ × SURð3Þ at classical level
Lattice simulations and effective model calculations show that, the magnetic field enhances the chiral symmetry breaking in vacuum which is called magnetic catalysis but reduces the critical temperature of the symmetry restoration which is called inverse magnetic catalysis [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
The parallel electromagnetic fields can break down the UAð1Þ symmetry [22,23], characterized by the pseudoscalar condensate hψiγ5τ3ψi via the electromagnetic triangle anomaly process π0 → 2γ
Summary
We systematically study quantum effect on chiral and UAð1Þ symmetry breaking under external electromagnetic fields in the frame of equal-time Wigner function formalism. The quark-antiquark condensate hψψi spontaneously breaks the SULð3Þ × SURð3Þ symmetry, and the UAð1Þ symmetry is broken by the quantum anomaly due to the nontrivial topology of the principal bundle of gauge field [1,2]. We effectively describe the quantum anomaly induced UAð1Þ symmetry breaking and spontaneous chiral symmetry breaking in a Nambu–Jona-Lasinio (NJL) model [36] at quark level [37,38,39,40,41] with scalar and pseudoscalar interaction channels. In the chiral limit with vanishing current quark mass m0 1⁄4 0 and vanishing electromagnetic fields, the Lagrangian density is with symmetry UVð1Þ × UAð1Þ × SULð2Þ × SURð2Þ. For the chiral symmetry SULð2Þ × SURð2Þ, it is explicitly broken down to ULð1Þ × URð1Þ by the electromagnetic fields, and the rest of the symmetry ULð1Þ × URð1Þ is spontaneously broken by
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
