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 v2, where v is the heavy-quark velocity in the quarkonium rest frame. Our numerical results are given for the J/ψ and (nS) channels, with n=1, 2, 3. The numerical results include a previously calculated correction of order αs and summations, to all orders in αs, of leading logarithms of mH2/mQ2, where mH is the Higgs-boson mass and mQ is the heavy-quark mass. These QCD corrections apply to the contribution of leading order in v and to part of the order-v2 correction. For the remainder of the order-v2 correction, we sum leading logarithms of mH/mQ through order αs2. These refinements reduce the theoretical uncertainties in the direct-production amplitudes for H→J/ψ+γ and H→(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.