Abstract
We explore the features of the UA(1) and chiral symmetry breaking of the Nambu–Jona-Lasinio model without the Kobayashi–Maskawa–'t Hooft determinant term in the presence of a parallel electromagnetic field. We show that the electromagnetic chiral anomaly can induce both finite neutral pion condensate and isospin-singlet pseudo-scalar η condensate and thus modifies the chiral symmetry breaking pattern. In order to characterize the strength of the UA(1) symmetry breaking, we evaluate the susceptibility associated with the UA(1) charge. The result shows that the susceptibility contributed from the chiral anomaly is consistent with the behavior of the corresponding η condensate. The spectra of the mesonic excitations are also studied.
Highlights
As is well known, the Lagrangian of the quantum chromodynamics (QCD) for light flavors (u, d quarks) has approximate S UA(2) chiral symmetry and UA(1) axial symmetry
We explore the features of the UA(1) and chiral symmetry breaking of the Nambu–Jona-Lasinio model without the Kobayashi-Maskawa-’t Hooft determinant term in the presence of a parallel electromagnetic field
We show that the electromagnetic chiral anomaly can induce both finite neutral pion condensate and isospin-singlet pseudo-scalar η condensate and modifies the chiral symmetry breaking pattern
Summary
The Lagrangian of the quantum chromodynamics (QCD) for light flavors (u, d quarks) has approximate S UA(2) chiral symmetry and UA(1) axial symmetry. [45], the effect of EM chiral anomaly (which should not be confused with the chiral anomaly due to gluons) on the chiral symmetry breaking and restoration was investigated in the parallel EM field (i.e., the EM field configuration with parallel electric and magnetic fields) and the isospin-triplet neutral pseudo-scalar π0 condensate was found to increase with the second Lorentz invariant I2 = E · B (without loss of generality, we will assume I2 ≥ 0) and to saturate at a critical I2c.
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