Radiative decays of the Higgs boson to apair of fermions

We revisit the radiative decays of the Higgs boson to a fermion pair h -> f (f) over bar gamma where f denotes a fermion in the Standard Model (SM). We include the chiralit-flipping diagrams via the Yukawa couplings at the order O(y(f)(2)alpha), the chirality-conserving contributions via the top-quark loops of the order O(y(t)(2)alpha(3)), and the electroweak loops at the order O(alpha(4)). The QED correction is about Q(f)(2) x O(1%) and contributes to the running of fermion masses at a similar level, which should be taken into account for future precision Higgs physics. The chirality-conserving electroweak-loop processes are interesting from the observational point of view. First, the branching fraction of the radiative decay h -> mu(+)mu(-)gamma is about a half of that of h -> mu(+)mu(-), and that of h -> e(+)e(-)gamma is more than four orders of magnitude larger than that of h -> e(+)e(-), both of which reach about 10(-4). The branching fraction of h -> 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 for the photon energy or the fermion pair invariant mass provide non-ambiguous discrimination for the underlying mechanisms of the Higgs radiative decay. We also study the process h -> c (c) over bar gamma and evaluate the observability at the LHC. We find it potentially comparable to the other related studies and better than the h -> J/psi gamma channel in constraining the charm-Yukawa coupling.