  The recent result by the OPERA experiment, confirming a trend already present
in a previous result by MINOS, raises the question of a possible strong
violation of standard relativity. In particular, the particles of the standard
model would have different critical speeds in vacuum, and such differences
would be measurable with nowadays facilities. Although several experimental and
phenomenological issues remain open, the situation deserves been studied
closely from a theoretical point of view. The data cannot be explained by
conventional extrapolations of Planck-scale Lorentz symmetry violation (LSV)
patterns. But, as already stressed in our previous papers since 1995, a weak
mixing of standard particles with superbradyons (particles with positive mass
and energy, and a critical speed in vacuum much larger than the speed of light)
can explain such an effect. Superbradyons can be the ultimate constituents of
matter (superluminal preons), but they may simultaneously exist in our Universe
as free particles just as light can cross a transparent material medium. In
this case, a direct mixing between superbradyons and the particles of the
standard model would be unavoidable. After briefly examining the experimental
situation and the problems it may raise, we comment on the possibility of a
superbradyonic mixing, as well as on the implications of a spinorial
description of space-time where space translations would form a SU(2) compact
group.
