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 upsilon(2), where upsilon is the heavy-quark velocity in the quarkonium rest frame. Our numerical results are given for the J/psi and Upsilon(nS) channels, with n = 1, 2, 3. The numerical results include a previously calculated correction of order alpha(s) and summations, to all orders in alpha(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 upsilon and to part of the order-upsilon(2) correction. For the remainder of the order-upsilon(2) correction, we sum leading logarithms of m(H)/m(Q) through order alpha(2)(s). These refinements reduce the theoretical uncertainties in the direct-production amplitudes for H --> J/psi + gamma and H --> Upsilon(1S) + gamma 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.