Higgs decay into a lepton pair and a photon revisited

We present new calculations of the differential decay rates for $H\to \ell^+\ell^- \gamma$ with $\ell=e$ or $\mu$ in the Standard Model. The branching fractions and forward-backward asymmetries, defined in terms of the flight direction of the photon relative to the lepton momenta, depend on the cuts on energies and invariant masses of the final state particles. For typical choices of these cuts we find the branching ratios $B(H\to e \bar e \gamma)=5.8\cdot 10^{-5}$ and $B(H\to \mu \bar \mu \gamma)=6.4\cdot 10^{-5}$ and the forward-backward asymmetries $\mathcal{A}^{(e)}_{\text{FB}}=0.343$ and $\mathcal{A}^{(\mu)}_{\text{FB}}=0.255$. We provide compact analytic expressions for the differential decay rates for the use in experimental analyses.