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

TL;DR

This work develops a systematic framework to study higher-order electroweak corrections to the angular observables in $h \to WW^* \to \ell^+ \nu_\ell \ell'^- \bar{\nu}_{\ell'}$, with a focus on quantum-entanglement interpretations via quantum tomography of the resulting two-qutrit system. Using density-matrix formalism and an irreducible-tensor basis, the authors quantify entanglement through concurrence bounds and extract angular coefficients at LO and NLO EW, finding shifts up to $\sim 5\%$ and the emergence of new structures that break LO relations. While NLO corrections deform the density matrix and can introduce negative eigenvalues, they remain milder in the $h \to WW^*$ channel than in $h \to e^+e^-\mu^+\mu^-$, preserving the two-qutrit interpretation to a good approximation under selected kinematic criteria. The results emphasize the necessity of including radiative corrections to reliably interpret collider observables as quantum-information features, and they highlight the WW$^*$ channel as comparatively robust for entanglement studies. Overall, the work advances precision Higgs phenomenology and the exploration of quantum properties in collider processes, offering guidance for both theory and experimental analyses.

Abstract

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. While higher-order effects influence the results, the two-qutrit quantum structure in the $h\to WW^*$ channel exhibits greater stability under such corrections than in the previously studied $h \to ZZ^*$ decay.

Figures (6)

• Figure 1: Representative sample of Feynman diagrams for the LO and NLO EW contributions to the Higgs boson decay into four leptons $h \rightarrow e^+ \nu_e \mu^- \bar{\nu}_{\mu}$.
• Figure 2: Lower $\mathscr{C}_{\mathrm{LB}}$ (red line) and upper $\mathscr{C}_{\mathrm{UB}}$ (blue line) bounds of the concurrence for $h\to WW^\ast\to e^+ \nu_e \mu^- \bar{\nu}_{\mu}$ at LO as a function of the lowest reconstructed invariant mass, $m_{W_2}<m_{W_1}$.
• Figure 3: Decay distribution for $h \rightarrow e^+ \nu_e \mu^- \bar{\nu}_{\mu}$ at LO (left panel), NLO EW (central panel), and their corresponding NLO/LO ratios (right panel) in the $m_{W_{1}}$-$m_{W_{2}}$ plane.
• Figure 4: Smallest eigenvalue of the density matrix $\rho_{\mathrm{NLO}}$ as a function of the two-dimensional distribution $(m_{W_2}, m_{W_1})$. The central panel shows the same quantity as a function of $m_{W_2}$ and the right panel displays it after imposing a cut on the reconstructed mass closest to the $W$ boson pole, $|m_{W_1} - m_W| < 10$ GeV. The left panel assumes the photon-lepton recombination criterion $\Delta R(\ell,\gamma)<0.1$, whereas the central and right panels display results for two possible criteria: $\Delta R(\ell,\gamma)<0.1$ (red) and $\Delta R(\ell,\gamma)<0.3$ (black).
• Figure 5: Lower $\mathscr{C}_{\mathrm{LB}}$ (left panel) and upper $\mathscr{C}_{\mathrm{UB}}$ (right panel) bounds of the concurrence for $h\to WW^\ast\to e^+ \nu_e \mu^- \bar{\nu}_{\mu}$ as a function of the off-shell $W$ mass, $m_{W_2}$. The results are presented at LO (black) and NLO EW with recombination radii $\Delta R(\ell,\gamma)<0.1$ (red) and $\Delta R(\ell,\gamma)<0.3$ (blue).