Relativistic corrections to Higgs boson decays to quarkonia

Understand

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 $J/\psi$ 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 $v$ and to part of the order-$v^2$ correction.