Relativistic corrections to Higgs boson decays to quarkonia

Abstract

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 $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}(nS)$ channels, with $n=1$, 2, 3. The numerical results include a previously calculated correction of order ${\ensuremath{\alpha}}_{s}$ and summations, to all orders in ${\ensuremath{\alpha}}_{s}$, 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 $v$ 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 ${\ensuremath{\alpha}}_{s}^{2}$. These refinements reduce the theoretical uncertainties in the direct-production amplitudes for $H\ensuremath{\rightarrow}J/\ensuremath{\psi}+\ensuremath{\gamma}$ and $H\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(1S)+\ensuremath{\gamma}$ 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.