Gauge invariant masses of pions in a strong magnetic field within Nambu--Jona-Lasinio model.
In this paper, we mainly study both neutral and charged pions' properties in a constant magnetic field $B$ at zero temperature within the Nambu--Jona-Lasinio model. By adopting the linear response theory based on imaginary-time path integral, we derive the correlation functions for pions in the coordinate space and the corresponding Schwinger phases show up automatically. The pole masses of charged pions are defined by their ground state energy following the conventions of lattice quantum chromodynamics. In this way, we are able to show the gauge invariance of the masses which increase monotonically with $B$ as expected.