Vetoing all the Higgs imposters in $H\to \ell^-\ell^+ Z$

Abstract

We develop an effective and methodical algorithm for the construction of general covariant four-point $H\ell\ell Z$ vertices, accommodating leptons $\ell=e, μ$, and designed to handle a boson $H$ of any integer spin, not merely confined to spins up to 2. While our numerical analysis assumes the $H$-boson mass to be $m_H=125\,{\rm GeV}$, the analytical framework we propose is versatile, enabling the examination of various mass as well as spin scenarios. These meticulously devised general covariant four-point $H\ell\ell Z$ vertices are pivotal in vetoing all the imposters of the Standard Model Higgs boson holding the spin-0 and even-parity quantum numbers, especially in one of its primary decay channels, the three-body decay process $H\to \ell^-\ell^+ Z$, observable at the Large Hadron Collider. Our innovative strategy encompasses the analysis of all the effectively allowed scenarios, extending beyond the limitations of previous investigations on the Higgs spin and parity determinations in the decay $H \to \ell^-\ell^+ Z$. Based on the significantly expanded scheme, we demonstrate that the Higgs boson imposter of any spin and parity can be definitively vetoed by leveraging threshold effects and angular correlations, even though achieving such conclusive results in practical and exhaustive analyses necessitates high event rates.