Radiative Decays of the Higgs Boson to a Pair of Fermions

We revisit the radiative decays of the Higgs boson to a fermion pair $h\rightarrow f\bar{f}\gamma$ in the Standard Model (SM). We include the chirality-flipping diagrams at the order $\mathcal{O}(y_f^2 \alpha)$, the chirality-conserving contributions at the order $\mathcal{O}(y_t^2 \alpha^3)$ and $\mathcal{O}(\alpha^4)$. The chirality-conserving electroweak-loop processes are interesting from the observational point of view. First, the branching fraction of the radiative decay $h \to \mu^+\mu^- \gamma$ is about a half of that of $h \to \mu^+\mu^-$, and that of $h \to e^+ e^- \gamma$ is more than four orders of magnitude larger than that of $h \to e^+ e^-$, both of which reach about $10^{-4}$. The branching fraction of $h \to \tau^+\tau^- \gamma$ is of the order $10^{-3}$. All the leptonic radiative decays are potentially observable at the LHC Run 2 or the HL-LHC. The kinematic distributions could provide non-ambiguous discrimination for the underlying mechanisms of the Higgs radiative decay. We also study the process $h \to c\bar c \gamma$ and evaluate the observability at the LHC. We find it potentially comparable to the other related studies and better than the $h \to J/\psi\ \gamma$ channel in constraining the charm-Yukawa coupling.