Addressing in nondimensional regularizations: a case study on the Bumblebee model

Ricardo J. C. Rosado; Adriano Cherchiglia; Marcos Sampaio; Brigitte Hiller

doi:10.1140/epjc/s10052-025-13756-3

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 41
https://doi.org/10.1140/epjc/s10052-025-13756-3

Regular Article - Theoretical Physics

Addressing $γ_{5}$ $\gamma _5$ in nondimensional regularizations: a case study on the Bumblebee model

Ricardo J. C. Rosado¹, Adriano Cherchiglia²^a, Marcos Sampaio³ and Brigitte Hiller¹

¹ CFisUC, Department of Physics, University of Coimbra, 3004-516, Coimbra, Portugal
² Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 777, Campinas, SP, Brazil
³ Universidade Federal do ABC, 09210-580, Santo André, Brazil

^a alche@unicamp.br

Received: 4 May 2024
Accepted: 23 December 2024
Published online: 21 January 2025

Abstract

We examine the subtleties of regularization schemes in four-dimensional space (4S), related in particular to the introduction of the $γ_{5}$ $\gamma _5$ matrix. To illustrate we use a “Bumblebee” model featuring dynamically induced Lorentz symmetry violation. The analysis centers on how different regularization methods affect the solutions to the gap equation in this model. We highlight the resolution of ambiguities associated with the $γ_{5}$ $\gamma _5$ matrix in ultraviolet divergent integrals by employing an enhanced Implicit Regularization (IREG) method. This method extends IREG to a quasi-four-dimensional space, $Q 4 S = 4 S \oplus X$ $Q4S = 4S \oplus X$ , drawing parallels with the consistent approach of Dimensional Reduction (DRED). Comparative analysis is conducted against results from the ’t Hooft–Veltman regularization scheme, conventional IREG in strict 4S, and sharp momentum cutoff techniques. Our results illustrate a scheme to compute $γ_{5}$ $\gamma _5$ interactions in physical dimension of divergent amplitudes, confirming the approach in Bruque et al. (JHEP 08:109, 2018).

© The Author(s) 2025

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