  It is usually expected that quantum gravity corrections will modify somehow
the symmetries of special relativity. In this paper we point out that the
possibility of very low-energy (with respect to the Planck energy)
modifications to special relativity in the framework of a deformed relativistic
theory is not ruled out, and that, depending on the value of that scale, such a
possibility could be tested in accelerator physics. In particular, we take a
simple example of a relativistic kinematics beyond special relativity from the
literature, and obtain a remarkable effect: two correlated peaks ("twin peaks")
associated to a single resonance. We analyze this phenomenology in detail, use
LEP data to put constraints of the order of TeV on the scale of corrections to
special relativity, and note that such an effect might be observable in a
future very high-energy proton collider.
