Is the Lorentz limiting speed equal to the Speed of Light? Photons vs Neutrino tests

We discuss the possibility that the limiting speed (c_l) appearing in Lorentz equations might be different i.e., slightly larger than the observed speed of light (c_n). We show that such a possibility can be tested by state-of-the-art Michelson-Morley experiments, but also by careful measurement of neutrino speeds. It would indeed suffice to show that c_n < c_neutrinos <= c_l. Quite interestingly, current limits from both approaches are competitive, in some circumstances. We also comment on competing tests using gamma-ray burst, assuming a dispersive character for the propagation of light.