Probing Unification Scenarios with Atomic Clocks

We make use of the comparison between measurements of various pairs of atomic clocks to impose constraints on coupled variations of fundamental constants in severs unification scenarios. We obtain null results for the proton-to-electron mass ratio ${\dot\mu}/{\mu}=(0.68\pm5.79)\times10^{-16}\, {\rm yr}{}^{-1}$ and for the gyromagnetic factor ${\dot g_p}/{g_p}=(-0.72\pm0.89)\times10^{-16}\, {\rm yr}{}^{-1}$ (both of these being at the 95% confidence level). These results are compatible with theoretical expectations on unification scenarios (which we briefly describe), but much freedom exists due to the presence of a degeneracy direction in the relevant parameter space.