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Relativistic corrections to Higgs boson decays to quarkonia

We improve the theoretical predictions for the decays of the Higgs boson to an $S$-wave vector quarkonium plus a photon by calculating the relativistic correction of order $v^2$, where $v$ is the heavy-quark velocity in the quarkonium rest frame. Our numerical results are given for the $J/ψ$ and $Υ(nS)$ channels, with $n=1,2,3$. The numerical results include a previously calculated correction of order $α_s$ and summations, to all orders in $α_s$, of leading logarithms of $m_H^2/m_Q^2$, where $m_H$ is the Higgs-boson mass and $m_Q$ is the heavy-quark mass. These QCD corrections apply to the contribution of leading order in $v$ and to part of the order-$v^2$ correction. For the remainder of the order-$v^2$ correction, we sum leading logarithms of $m_H/m_Q$ through order $α_s^2$. These refinements reduce the theoretical uncertainties in the direct-production amplitudes for $H \to J/ψ+γ$ and $H \to Υ(1S)+γ$ by approximately a factor of 3 and open the door to improved determinations at the LHC of the Higgs-boson Yukawa couplings to the charm and bottom quarks.