Quantum Tomography and Entanglement in Semi-Leptonic $h\to V{V}^{\ast }$ Decays at Higher Orders

Abstract

Angular correlations in Higgs decays to electroweak gauge bosons, $h\to Z{Z}^{\ast },W{W}^{\ast }$, provide a powerful probe of both new physics effects and quantum information observables. We present a systematic study of semi-leptonic Higgs decays $h\to V{V}^{\ast }\to {\ell }^{+}{\ell }^{-}q\bar{q}$ and ${\ell }^{\pm }{\nu }_{\ell }q{\bar{q}}^{\prime }$, including finite final state fermion masses, NLO QCD, and NLO electroweak corrections. We show that finite final state quark masses can induce effects that go beyond the two-qutrit description in more inclusive regimes, while remaining controllable with suitable kinematic selections. QCD corrections lead to modest percent-level shifts, whereas electroweak corrections can significantly modify the angular structure, particularly in the $h\to Z{Z}^{\ast }$ channels. We assess the impact of these effects on the reconstructed density matrix and entanglement measures, finding that, although they modify the angular observables, the semi-leptonic channels are better approximated by a two-qutrit description than the fully leptonic decay $h\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$.

Comments: Minor revisions after review for publication. 27 pages, 7 figures and 13 tables