Measuring the Higgs spin and parity in H→ ⁻⁺ Z

We develop an effective and methodical algorithm for the construction of general covariant four-point H Z vertices, accommodating leptons =e, μ, and designed to handle a Higgs boson H of any integer spin, not merely confined to spins up to 2. While our numerical analysis assumes the Higgs boson mass to be mH=125\, GeV, the analytical framework we propose is versatile, enabling the examination of various mass scenarios. These meticulously devised general covariant four-point H Z vertices are pivotal in the systematic determination of the spin and parity of the Standard Model Higgs boson, especially via one of its primary decay channels, the three-body decay process H→ ⁻⁺ Z, observable at the Large Hadron Collider. Our innovative strategy extends beyond the limitations of previous investigations on the Higgs spin and parity determinations. It not only encompasses the analysis of the two-step cascade decay H→ Z^ Z → ⁻⁺ Z, featuring an intermediate virtual Z^ exchange but also integrates consideration for the direct 4-point contact H Z interaction. Our significantly expanded scheme provides a definitive and unequivocal platform for determining and confirming the spinless nature and even parity of the SM Higgs boson by leveraging threshold effects and angular correlations, even though achieving such conclusive results in practical and exhaustive analyses necessitates high event rates.