Angular and invariant-mass observables in the four-body Higgs decay htoellbar{ν}_ellbar{ell}^primeν_(ell^prime)

We study the angular distribution of the Higgs boson decay $h\to\ell\bar{\nu}_\ell\bar{\ell}^\prime\nu_{\ell^\prime}$ with $\ell\neq\ell^\prime$. Due to the presence of two undetected neutrinos, a complete angular analysis is not feasible at experiments. To overcome this, we reorganize the kinematics from the conventional lepton-neutrino pairs into a charged-lepton pair and a neutrino pair, i.e.~$\ell\bar{\ell}^\prime$ and $\bar{\nu}_\ell\nu_{\ell^\prime}$. This allows us to express the differential decay rate in terms of experimentally accessible variables, including the invariant mass squared of the neutrino pair. Using the effective field theory framework, we derive this rate and integrate over the neutrino-associated angles. This parametrization provides a clean and measurable angular distribution, offering a new probe of the $hWW$ coupling and possible beyond-the-Standard-Model contributions.