Analysis of final state lepton polarization-dependent observables in H → ℓ⁺ℓ⁻γ in the SM at loop level

Recently, the CMS and ATLAS collaborations have announced the results for H → Z[→ ℓ⁺ℓ⁻]γ with ℓ = e or μ [1, 2], where H → Zγ is a sub-process of H → ℓ⁺ℓ⁻γ. This semi-leptonic Higgs decay gets both resonant and non-resonant contributions from the loop-induced H → Z[→ ℓ⁺ℓ⁻]γ. To probe further features coming from these contributions to H → ℓ⁺ℓ⁻γ, we argue that the polarization of the final state leptons is also an important parameter. We show that the interference of resonant and non-resonant contributions, which is negligible in the case of unpolarized leptons, plays a significant role when considering the polarization of the final state lepton. For this purpose, we have calculated the polarized decay rates and the longitudinal (P_L), normal (P_N), and transverse (P_T) polarization asymmetries. We find that these asymmetries purely come from the loop contributions and are helpful to further investigate the resonant and non-resonant nature of H → Z[→ ℓ⁺ℓ⁻]γ decay. We observe that for ℓ = e, μ, the longitudinal decay rate is highly suppressed around m_ℓℓ ≈ 60 GeV when the final lepton spin is $-\frac{1}{2}$ \( -\frac{1}{2} \) , dramatically increasing the corresponding lepton polarization asymmetries. Furthermore, we analyze another observable, the ratio of decay rates $R_{i\pm }^{{\mathcal{ll}}^{\prime }}$ \( {R}_{i\pm}^{{\mathcal{ll}}^{\prime }} \) , where ℓ and ℓ^′ refer to different final state lepton generations. Precise measurements of these observables at the HL-LHC and the planned e⁺e⁻ collider can provide fertile ground to test not only the SM but also to examine the signatures of possible NP beyond the SM.