Charged meson masses under strong magnetic fields: gauge invariance and Schwinger phases

Abstract

We study the role of the Schwinger phase (SP) that appears in the propagator of a charged particle in the presence of a static and uniform magnetic field $\vec{B}$. We first note that this phase cannot be removed by a gauge transformation; far from this, we show that it plays an important role in the restoration of the symmetries of the system. Next, we analyze the effect of SPs in the one-loop corrections to charged pion and rho meson selfenergies. To carry out this analysis we consider first a simple form for the meson-quark interactions, and then we study the ${\pi }^{+}$ and ${\rho }^{+}$ propagators within the Nambu-Jona-Lasinio model, performing a numerical analysis of the $B$ dependence of meson lowest energy states. For both ${\pi }^{+}$ and ${\rho }^{+}$ mesons, we compare the numerical results arising from the full calculation -- in which SPs are included in the propagators, and meson wavefunctions correspond to states of definite Landau quantum number -- and those obtained within alternative schemes in which SPs are neglected (or somehow eliminated) and meson states are described by plane waves of definite four-momentum.

56 pages, 2 figures

References in corpus (7)

• The Chiral Magnetic Effect
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model
• Charged and neutral vector meson under magnetic field
• Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: mixing effects
• Charged pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model
• Physical symmetries and gauge choices in the Landau problem

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• Spectral function for pions in magnetic field