Higgs boson decay into a lepton pair and a photon: A roadmap to the discovery of H →zγ and probes of new physics

The decay H→ℓ$^{+}$ℓ$^{–}$γ, ℓ=e, μ receives contributions from H→Z[→ℓ$^{+}$ℓ$^{–}$]γ and a nonresonant contribution, both of which are loop induced. We describe how one can separate these subprocesses in a gauge-independent way, define the decay rate Γ(H→Zγ), and extract the latter from differential H→ℓ$^{+}$ℓ$^{–}$γ branching ratios. For ℓ=μ, also the tree decay rate, which is driven by the muon Yukawa coupling, is important. We propose kinematic cuts optimized to separate the three contributions, paving the way to the milestone (i) discovery of H→Zγ, (ii) discovery of H→μ$^{+}$μ$^{–}$γ| $_{tree}$, and (iii) quantification of new physics in both the effective H−Z−γ and nonresonant H−ℓ$^{+}$ℓ$^{–}$−γ couplings.