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arXiv · 2304.12933

Renormalization of Very Special Relativity gauge theories

Jorge Alfaro
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Abstract

Mandelstam-Leibbrandt(ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors $n_\mu,\bar{n}_\mu$ besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector $\bar{n}_\mu$ destroys the $Sim(2)$ symmetry of the VSR model. We devise a systematic procedure to take the $\bar{n}_\mu->0$ limit to recover the lost $Sim(2)$ symmetry. The procedure produces $Sim(2)$ and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics(VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications.

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Jorge Alfaro. 2023-04-24. Renormalization of Very Special Relativity gauge theories. https://doi.org/10.1007/jhep06(2023)003

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