Complex bumblebee model
Willian Carvalho, A. C. Lehum, J. R. Nascimento, A. Yu. Petrov

TL;DR
This paper develops a renormalizable complex bumblebee model coupled to gauge fields, analyzing its quantum corrections, renormalization group behavior, and potential for dynamical Lorentz symmetry breaking.
Contribution
It introduces a complex extension of the bumblebee theory with new couplings, computes one-loop divergences, and explores vacuum structure via an RG-covariant effective potential.
Findings
Derived one-loop UV divergences and counterterms for the model.
Calculated RG functions for couplings and self-interactions.
Identified conditions for dynamical Lorentz symmetry breaking via dimensional transmutation.
Abstract
We formulate a renormalizable complex extension of the bumblebee theory in which the bumblebee field is promoted to a complex one and coupled to an Abelian gauge sector. Besides the minimal gauge covariant interaction, the model includes a longitudinal kinetic term controlled by a dimensionless parameter and a non-minimal magnetic-type coupling between the complex bumblebee and the photon. Using dimensional regularization and minimal subtraction, we determine the one-loop UV divergences of the two-, three-, and four-point functions relevant to the renormalization of the gauge, longitudinal, and quartic sectors. We obtain the corresponding counterterms and derive the one-loop renormalization-group functions for , , , and the bumblebee self-couplings and . Motivated by the known gauge- and field-reparametrization subtleties of the…
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