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arXiv · 2603.26529

Complex bumblebee model

Willian Carvalho·A. C. Lehum·J. R. Nascimento·A. Yu. Petrov
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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 $g_l$ and a non-minimal magnetic-type coupling $g_m$ 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 $e$, $g_l$, $g_m$, and the bumblebee self-couplings $\lambda$ and $\tilde\lambda$. Motivated by the known gauge- and field-reparametrization subtleties of the conventional Coleman--Weinberg analysis, we formulate an RG-covariant leading-logarithmic improvement scheme for the Vilkovisky--DeWitt effective potential in normal field coordinates, in which the RG operator is governed solely by the beta functions. We apply this framework to a real constant bumblebee background and obtain the leading-logarithmic one-loop effective potential, discussing the conditions under which a nontrivial vacuum is generated by dimensional transmutation and thereby provides a dynamical realization of Lorentz symmetry breaking in this class of models.

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Willian Carvalho, A. C. Lehum, J. R. Nascimento, A. Yu. Petrov. 2026-03-27. Complex bumblebee model. https://doi.org/10.1103/437b-8nlz

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