Polarization-Dependent Observables in <i>H</i> → ℓ+ ℓ– γ in the SM

Abstract The rare three-body decay of a Higgs boson to a lepton–antilepton pair and a photon has begun to attract attention, after the first evidence for the $H\rightarrow Z\gamma$ channel at CMS and ATLAS, which is a subprocess of $H \rightarrow \ell ^+ \ell ^- \gamma$. To investigate some important features of this process, we suggest that the polarized forward-backward and the photon polarization asymmetries could be useful to probe its important properties, such as the behavior of Yukawa coupling, resonance, and nonresonance contributions. Our analysis introduces a comprehensive framework to evaluate the aforementioned polarization-dependent observables. By analyzing the polarization effects of the final-state photon and lepton separately on forward-backward asymmetries, we demonstrate that loop-induced contributions play a significant role in investigating these asymmetries. Unlike the unpolarized case, where the interference effects of resonance and nonresonance effects are minimal, we show that polarization-dependent observables offer a powerful tool to analyze these features of this decay mode. Furthermore, these observables can provide a handy tool for probing possible signatures of physics beyond the SM.