Higher-Order Corrections to Quantum Observables in $h\to WW^*$

The Higgs boson decay $h \to WW^* \to \ell^+ ν_\ell \ell'^- \barν_{\ell'}$ provides a unique window into the structure of the Higgs couplings to electroweak gauge bosons and has recently gained attention for its potential to unveil quantum properties such as quantum entanglement between the intermediate gauge bosons. In this work, we present a systematic study of next-to-leading order electroweak corrections to the angular coefficients characterizing this decay. While these coefficients are highly constrained at leading order, radiative corrections induce shifts of up to 5% to the existing terms and generate novel structures that vanish at leading order, breaking previous relations among coefficients. Despite the impact of these higher-order effects, the $h\to WW^*$ channel exhibits greater stability under higher-order corrections compared to the previously studied $h \to ZZ^*$ decay, better preserving the underlying two-qutrit quantum structure.