Two-loop QCD corrections to Higgs radiative decay to vector quarkonium

The exclusive production of $J\mathrm{/}\psi$ through Higgs boson radiative decay may serve a clean channel to extracting the charm quark Yukawa coupling. We calculate the two-loop QCD corrections to $H\to J\mathrm{/}\psi (\mathrm{{\rm Y}})+\gamma$ using an optimized nonrelativistic QCD (NRQCD) approach. We compute the $\mathcal{O}({\alpha }_s^2)$ correction in the direct channel, where Higgs directly couples to $c\bar{c}$, as well as the $\mathcal{O}({\alpha }_s)$ correction in the indirect channel, {\it viz.}, $H\to {\gamma }^{\ast }\gamma$ followed by the virtual photon fragmentation into $J\mathrm{/}\psi$. Incorporating the destructive interference between the direct and indirect channels, we present to date the most accurate predictions for Higgs boson radiative decay into vector quarkonium, $\mathcal{B}(H\to J\mathrm{/}\psi +\gamma )=3.27_{-0.07}^{+0.30}{}_{-0.06}^{+0.06}{}_{-0.13}^{+0.13}\times {10}^{-6}$, and $\mathcal{B}(H\to \mathrm{{\rm Y}}+\gamma )=1.34_{-0.31}^{+0.75}{}_{-0.20}^{+0.25}{}_{-0.05}^{+0.05}\times {10}^{-8}$.