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Two-loop renormalization of the CPT-even Lorentz-violating scalar QED

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Abstract

Investigating quantum effects arising from high loops in perturbation theory is crucial for the physical applications of any quantum field theory. This paper presents a comprehensive analysis of the two-loop renormalization of CPT-even Lorentz-violating scalar electrodynamics at the first order in the background vectors. We provide results for the self-energies of the photon and scalar field, as well as for the three-point function associated with the scalar–scalar–photon vertex, ensuring a thorough examination of the quantum effects. The asymptotic behavior of the model is investigated through the calculation of the beta functions, and the Ward identities are fulfilled, demonstrating the consistency of the result. Computational tools were employed to carry out the calculations, and we provide additional details in the Supplemental Material for interested readers.

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Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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Acknowledgements

The authors are grateful to M. Gomes and J. R. Nascimento for important discussions. The work of A. Yu. P. has been partially supported by the CNPq project No. 301562/2019-9. The work of A. C. L. has been partially supported by the CNPq project No. 404310/2023-0.

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Authors and Affiliations

  1. Departamento de Física, Instituto de Ciências Naturais, Universidade Federal de Lavras, Caixa Postal 3037, Lavras, Minas Gerais, 37200-900, Brazil

    L. C. T. Brito

  2. Instituto de Engenharia, Ciência e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, Avenida Um, 4050, Cidade Universitária, Janaúba, Minas Gerais, 39447-790, Brazil

    J. C. C. Felipe

  3. Departamento de Estatística, Física e Matemática, Universidade Federal de São João del Rei, Rod. MG-443, Km 7, Fazenda do Cadete, Ouro Branco, Minas Gerais, 36497-899, Brazil

    J. C. C. Felipe

  4. Faculdade de Física, Universidade Federal do Pará, Belém, Pará, 66075-110, Brazil

    A. C. Lehum

  5. Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba, 58051-970, Brazil

    A. Yu. Petrov

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  1. L. C. T. Brito
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Correspondence to A. Yu. Petrov.

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Brito, L.C.T., Felipe, J.C.C., Lehum, A.C. et al. Two-loop renormalization of the CPT-even Lorentz-violating scalar QED. Eur. Phys. J. Plus 139, 90 (2024). https://doi.org/10.1140/epjp/s13360-024-04891-z

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