Electroweak standard model with very special relativity

The very special relativity electroweak Standard Model (VSR EW SM) is a theory with $\mathrm{SU}(2{)}_L\times \mathrm{U}(1{)}_R$ symmetry, with the same number of leptons and gauge fields as in the usual Weinberg-Salam model. No new particles are introduced. The model is renormalizable and unitarity is preserved. However, photons obtain mass and the massive bosons obtain different masses for different polarizations. Besides, neutrino masses are generated. A VSR-invariant term will produce neutrino oscillations and new processes are allowed. In particular, we compute the rate of the decays $\mu \to e+\gamma$. All these processes, which are forbidden in the electroweak Standard Model, put stringent bounds on the parameters of our model and measure the violation of Lorentz invariance. We investigate the canonical quantization of this nonlocal model. Second quantization is carried out, and we obtain a well-defined particle content. Additionally, we do a counting of the degrees of freedom associated with the gauge bosons involved in this work, after spontaneous symmetry breaking has been realized. Violations of Lorentz invariance have been predicted by several theories of quantum gravity [J. Alfaro, H. Morales-Tecotl, and L. F. Urrutia, Phys. Rev. Lett. 84, 2318 (2000); Phys. Rev. D 65, 103509 (2002)]. It is a remarkable possibility that the low-energy effects of Lorentz violation induced by quantum gravity could be contained in the nonlocal terms of the VSR EW SM.

Figure 1

$X$ decay to $Y$ plus photon, where $(X,Y)=(e,\tau ,\mu )$ and $m_X>m_Y$.

Figure 2

$X$ decay to $Y$ plus neutrino-antineutrino, where $(X,Y)=(e,\tau ,\mu )$ and $m_X>m_Y$.