Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model
Abstract We examine the subtleties of regularization schemes in four-dimensional space (4S), related in particular to the introduction of the $$\gamma _5$$ γ 5 matrix. To illustrate we use a “Bumblebee” model featuring dynamically induced Lorentz symmetry violation. The analysis centers on how diffe...
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| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13756-3 |
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| author | Ricardo J. C. Rosado Adriano Cherchiglia Marcos Sampaio Brigitte Hiller |
| author_facet | Ricardo J. C. Rosado Adriano Cherchiglia Marcos Sampaio Brigitte Hiller |
| author_sort | Ricardo J. C. Rosado |
| collection | DOAJ |
| description | Abstract We examine the subtleties of regularization schemes in four-dimensional space (4S), related in particular to the introduction of the $$\gamma _5$$ γ 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 $$\gamma _5$$ γ 5 matrix in ultraviolet divergent integrals by employing an enhanced Implicit Regularization (IREG) method. This method extends IREG to a quasi-four-dimensional space, $$Q4S = 4S \oplus X$$ Q 4 S = 4 S ⊕ 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 $$\gamma _5$$ γ 5 interactions in physical dimension of divergent amplitudes, confirming the approach in Bruque et al. (JHEP 08:109, 2018). |
| format | Article |
| id | doaj-art-8ec992636f99486bb606d43d8caad221 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-8ec992636f99486bb606d43d8caad2212025-01-26T12:49:37ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-01-0185111310.1140/epjc/s10052-025-13756-3Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee modelRicardo J. C. Rosado0Adriano Cherchiglia1Marcos Sampaio2Brigitte Hiller3CFisUC, Department of Physics, University of CoimbraInstituto de Física Gleb Wataghin, Universidade Estadual de CampinasUniversidade Federal do ABCCFisUC, Department of Physics, University of CoimbraAbstract We examine the subtleties of regularization schemes in four-dimensional space (4S), related in particular to the introduction of the $$\gamma _5$$ γ 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 $$\gamma _5$$ γ 5 matrix in ultraviolet divergent integrals by employing an enhanced Implicit Regularization (IREG) method. This method extends IREG to a quasi-four-dimensional space, $$Q4S = 4S \oplus X$$ Q 4 S = 4 S ⊕ 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 $$\gamma _5$$ γ 5 interactions in physical dimension of divergent amplitudes, confirming the approach in Bruque et al. (JHEP 08:109, 2018).https://doi.org/10.1140/epjc/s10052-025-13756-3 |
| spellingShingle | Ricardo J. C. Rosado Adriano Cherchiglia Marcos Sampaio Brigitte Hiller Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model European Physical Journal C: Particles and Fields |
| title | Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model |
| title_full | Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model |
| title_fullStr | Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model |
| title_full_unstemmed | Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model |
| title_short | Addressing $$\gamma _5$$ γ 5 in nondimensional regularizations: a case study on the Bumblebee model |
| title_sort | addressing gamma 5 γ 5 in nondimensional regularizations a case study on the bumblebee model |
| url | https://doi.org/10.1140/epjc/s10052-025-13756-3 |
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