Apparent Lorentz violation with superluminal Majorana-tachyonic neutrinos at OPERA?

From the controversial data release of the OPERA–CNGS experiment (The OPERA collaboration 2011 arXiv:1109.4897), publicly announced on 23 September 2011 where muonic neutrinos seem to propagate at a speed faster than light, we cast a phenomenological model describing the behaviour of such a tachyonic neutrino, carrying an imaginary mass based on the Majorana tower of particles described in 1932. If the interpretation of OPERA data is correct and considering the strong constraints from the observations of the supernova SN1987a, we show that the tachyonic behaviour of the neutrino can occur only when it is propagating inside matter. Following this idea, within the experimental errors, we fit the data released by OPERA with those of MINOS and by assuming a superluminal propagation inside the matter of SN1987a, confirm our ansatz with stellar structure models of the supernova precursor. Monte Carlo simulations based on this fit agree well with the new OPERA data. Possible violations of Lorentz invariance due to quantum gravity effects have been considered.