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The decay $H\to \ell^+\ell^- \gamma$, $\ell=e,\mu$, receives contributionsfrom $H\to Z[\to \ell^+\ell^-] \gamma$ and a non-resonant contribution, both ofwhich are loop-induced. We describe how one can separate these sub-processes ina gauge-independent way, define the decay rate $\Gamma(H\to Z\gamma)$, andextract the latter from differential $H\to \ell^+\ell^- \gamma$ branchingratios. For $\ell=\mu$ also the tree decay rate, which is driven by the muonYukawa coupling, is important. We propose kinematic cuts optimized to separatethe three contributions, paving the way to the milestones (i) discovery of$H\to Z \gamma$, (ii) discovery of $H\to \mu^+\mu^- \left. \gamma\right|_{\rmtree}$, and (iii) quantification of new physics in both the effective$H$-$Z$-$\gamma$ and non-resonant $H$-$\ell^+$-$\ell^-$-$\gamma$ couplings.

Higgs decay into a lepton pair and a photon: a roadmap to $\mathbf{H\to Z\gamma}$ discovery and probes of new physics