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Recently, both ATLAS and CMS measured the decay $h\to\mu^+\mu^-$, finding asignal strength with respect to the Standard Model expectation of $1.2\pm0.6$and $1.19\substack{+0.41+0.17\\-0.39 -0.16}$, respectively. This provides, forthe first time, evidence that the Standard Model Higgs couples to secondgeneration fermions. This measurement is particularly interesting in thecontext of the intriguing hints for lepton flavor universality violation,accumulated within recent years, as new physics explanations could also betested in the $h\to\mu^{+}\mu^{-}$ decay mode. Leptoquarks are prime candidatesto account for the flavor anomalies. In particular, they can provide thenecessary chiral enhancement (by a factor $m_t/m_\mu$) to address $a_\mu$ withTeV scale new physics. In this letter we point out that such explanations of$a_\mu$ also lead to enhanced effects in $h\to\mu^+\mu^-$ and we examine thecorrelations between $h\to\mu^+\mu^-$ and $a_\mu$ within leptoquark models. Wefind that the effect in the branching ratio of $h\to\mu^+\mu^-$ ranges fromseveral percent up to a factor three, if one aims at accounting for $a_\mu$ atthe $2\,\sigma$ level. Hence, the new ATLAS and CMS measurements alreadyprovide important constraints on the parameter space, rule out specific $a_\mu$explanations and will be very important to test the flavor anomalies in thefuture.

Correlating $h\to\mu^+\mu^-$ to the Anomalous Magnetic Moment of the Muon via Leptoquarks