Testing Grand Unification at the (S)LHC

We examine the possibility of measuring the three gauge couplings at high scales at the LHC, in order to see the first steps as they run toward Grand Unification at much higher energies. Using the MSSM with sparticle masses of several hundred GeV as an example of a theory in which the couplings do unify at very high energies, we find that the processes pp->lv, pp->l+l- and pp->gamma+j can be useful to discriminate the SM from the MSSM with masses at the few hundred GeV scale, and determine that the couplings are converging at better than the SM prediction toward the GUT scale. Such measurements indirectly probe the existence of lower mass states, charged under the SM gauge groups, but which may be difficult to produce directly or extract from backgrounds at the LHC.