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arXiv · 2306.04128

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

D. Gomez Dumm·S. Noguera·N. N. Scoccola
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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.

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D. Gomez Dumm, S. Noguera, N. N. Scoccola. 2023-06-07. Charged meson masses under strong magnetic fields: gauge invariance and Schwinger phases. https://doi.org/10.1103/physrevd.108.016012

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