Feynman Rules, Ward Identities and Loop Corrections in Very Special Relativity Standard Model

In this paper, we want to study one loop corrections in Very Special Relativity Standard Model(VSRSM). In order to satisfy the Ward identities and the $Sim\left(2\right)$ symmetry of the model, we have to specify the Feynman rules, including the infrared regulator. To do this, we adapt the Mandelstam–Leibbrandt (ML) prescription to incorporate external momentum-dependent null vectors. As an example, we use the new $Sim\left(2\right)$ invariant dimensional regularization to compute one loop corrections to the effective action in the subsector of the VSRSM that describe the interaction of photons with charged leptons. New stringent bounds for the masses of ${\nu }_e$ and ${\nu }_{\mu }$ are obtained.