Nambu–Jona-Lasinio model in a parallel electromagnetic field

We explore the features of the $U_A(1)$ 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 $\eta$ condensate and thus modifies the chiral symmetry breaking pattern. In order to characterize the strength of the $U_A(1)$ symmetry breaking, we evaluate the susceptibility associated with the $U_A(1)$ charge. The result shows that the susceptibility contributed from the chiral anomaly is consistent with the behavior of the corresponding $\eta$ condensate. The spectra of the mesonic excitations are also studied.