Proton's half life has a lower estimated bound in 10^33 years aprox. This is due to the enormous mass of the X boson, predicted by some GUTs. So my question is: if the free proton is in a high energy state, it has more energy (ready to be "used") and thus it would be easier to create the X boson needed. Is this implying a energy-dependent half life? If so, has this dependence been calculated somewhere? I'd love to have some references if possible. Sorry for my english and thanks.
All decays behave the same way, the mass of the mediating particle affects the lifetime when measured at the rest frame.
The lifetime of the muon for example is given as ~2.2μsec, this number is for a muon at rest. Energetic muons are relativistic, and so time dilation of a high energy muon will give a longer lifetime according to the relativistic effects.
The same would be true for the possible proton decay, except that the mass of the X, ~10^15 GeV is so huge and the lifetime this implies (~10^33 seconds) so large the probability of decay could not be enhanced in the existing accelerators.