Vetoing all the Higgs imposters in H→ℓ-ℓ+Z

We develop an effective and methodical algorithm for the construction of general covariant four-point HℓℓZ vertices, accommodating leptons ℓ=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=125GeV, 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 HℓℓZ 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→ℓ^-ℓ⁺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→ℓ^-ℓ⁺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 angular and invariant mass distributions focusing on threshold effects. Even though achieving such conclusive results in practical and exhaustive analyses may necessitate high event rates, especially in the spin-0 contact-interaction case.