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We make use of the comparison between measurements of various pairs of atomicclocks to impose constraints on coupled variations of fundamental constants insevers unification scenarios. We obtain null results for the proton-to-electronmass ratio ${\dot\mu}/{\mu}=(0.68\pm5.79)\times10^{-16}\, {\rm yr}{}^{-1}$ andfor 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). Theseresults are compatible with theoretical expectations on unification scenarios(which we briefly describe), but much freedom exists due to the presence of adegeneracy direction in the relevant parameter space.

Probing Unification Scenarios with Atomic Clocks