Relativistic corrections to Higgs boson decays to quarkonia

TL;DR

This paper refines theoretical predictions for Higgs decays to quarkonia plus a photon by calculating relativistic and QCD corrections, reducing uncertainties and aiding Higgs Yukawa coupling measurements at the LHC.

Contribution

It introduces the calculation of relativistic $v^2$ corrections and resummation of leading logarithms, enhancing the precision of Higgs decay predictions to quarkonia.

Findings

Reduced theoretical uncertainties by a factor of 3.

Improved predictions for $H o J/+\u03b3$ and $H o (1S)+$ decays.

Facilitates more accurate determination of Higgs-quark Yukawa couplings.

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 $J/\psi$ 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. For the remainder of the order-$v^2$ correction, we sum leading logarithms of $m_H/m_Q$ through order $\alpha_s^2$. These refinements reduce the theoretical uncertainties in the direct-production amplitudes for $H \to J/\psi+\gamma$ and $H \to \Upsilon(1S)+\gamma$ 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.