On the possibility of superluminal neutrino propagation

We analyze the possibility of superluminal neutrino propagation δv≡(v−c)/c>0 as indicated by OPERA data, in view of previous phenomenological constraints from supernova SN1987a and gravitational Čerenkov radiation. We argue that the SN1987a data rule out δv∼(Eν/MN)N for N⩽2 and exclude, in particular, a Lorentz-invariant interpretation in terms of a 'conventional' tachyonic neutrino. We present two toy Lorentz-violating theoretical models, one a Lifshitz-type fermion model with superluminality depending quadratically on energy, and the other a Lorentz-violating modification of a massless Abelian gauge theory with axial-vector couplings to fermions. In the presence of an appropriate background field, fermions may propagate superluminally or subluminally, depending inversely on energy, and on direction. Reconciling OPERA with SN1987a would require this background field to depend on location.