When travelling over the 730 kilometers from the large hadron collider to OPERA neutrino detector, neutrinos where observed to travel faster than light by a factor of 2.5*10^-5, arriving some 60 nanoseconds early. The statistics of the result have been described here by Tommaso, and although the evidence is quite strong, this is the first result from mainstream physics ever to challenge Einsteins special theory of relativity, and was greeted was some skepticism, but follow up results, in November again showed the same velocity.
In fact Special relativity doesn't state that nothing came travel faster than light. SR prevents slower than light, massive particle every travelling at or above the speed of light, and restricts massless particles to travelling at exactly the speed of light. But SR does allow particles where the square of the mass is negative, known as tachyons that travel faster than light to exist.
Requiring cause and effect to be, effect follows cause, i.e that effect is the future light cone of cause, and preventing information travelling faster than light can still be done in case of tachyons by having the direction of tachyon reversed according to how faster the observer is travelling.
Tachyon theory doesn't seem to match the OPERA results though, for three reasons.
Tachyons would emit a kind of sonic boom, in the wake called Cherenkov radiation, and rapidly loss energy, no such energy loss was observed. The Tachyon mass of the neutrino would be in the 100 MeV range, and mass than large would have been observed in pion decay.
A Tachyon would move slower, i.e. closer to light speed (from above), the higher its energy. OPERA saw the same velocity for energies from 10 to about 40 billion electron volts.
I seen quite a few theories published at arXiv and even one at from Sasha at Science 2.0, trying to fit the results, but none so far that seem to fit in with rest of physics. However i'll write here about three different theories based only on physics written prior to the OPERA experiment. The first is one I printed on my other axitronics blog, just two weeks after the results.
I was already working on a theory given neutrinos an new force, in which they have a simple charge that reverses when the spin changes from left handed to right handed, and I remembered an effect from quantum field theory, which makes particles travel slightly faster than light when they move through a region of space where there field they interact with has a negative energy, i.e. where there are less modes of the field than would exist in empty space, a Casmir vacuum. This effect was first shown mathematical by K Scharnhorst and also suggested as a cause of faster than light neutrinos by Karl Svozil although he did not have a theory of a force between neutrinos.
The Scharnhost effect in velocity, depends linearly on the energy density of some field, and the inversely as the forth power of mass of the lightest fermions in interacting with the field. Its was orginally formulated in QED, where a photon has chance to spend some of its time as a electron and positron while travelling. It turns out that the speed is of photon doesn't get altered in a vacuum, but if there is an electric or magnetic field other than the photon, it will make a difference to the photons speed.
The effect is tiny in QED for normal energies because the mass of the electron is so large. The mass of known neutrinos is tiny, certainly less than .06 eV, and this means the speed increase of neutrinos can be much larger. If matter is crowded with light neutrinos at low speed, most of the energy levels for a field quanta interacting with neutrinos will be blocked, make a Casmir type vaccum containing less energy than a standard vacuum. EM energy and the mass energy of the matter, doesn't matter here, only the energy of a massless field that interacts with neutrinos.
If its Scharnhost effect producing the speed up of neutrino in matter. The asympotic velocity of neutrinos depends only the density of matter between CERN and OPERA and possibly it temperature. And not on the energy or type of neutrino. To test if this is the true cause, experimenters need to compare the travel times of neutrinos though various materials.