Flavor-Changing Higgs Decays in Grand Unification with Minimal Flavor Violation

We consider the flavor-changing decays of the Higgs boson in a grand unified theory framework which is based on the SU(5) gauge group and implements the principle of minimal flavor violation. This allows us to explore the possibility of connecting the tentative hint of the Higgs decay $h\to\mu\tau$ recently reported in the CMS experiment to potential new physics in the quark sector. We look at different simple scenarios with minimal flavor violation in this context and how they are subject to various empirical restrictions. In one specific case, the relative strengths of the flavor-changing leptonic Higgs couplings are determined mainly by the known quark mixing parameters and masses, and a branching fraction ${\cal B}(h\to\mu\tau)\sim1\%$ is achievable without the couplings being incompatible with the relevant constraints. Upcoming data on the Higgs leptonic decays and searches for the $\mu\to e\gamma$ decay with improved precision can offer further tests on this scenario.