Beyond Geolocating: Constraining Higher Dimensional Operators in $H \to 4\ell$ with Off-Shell Production and More

TL;DR

This work enlarges the Higgs–ZZ coupling program by (i) including off-shell $gg\to H^*\to ZZ\to 4\ell$ production and (ii) incorporating the complete five-operator basis up to dimension five for the $XZZ$ vertex. It provides analytic off-shell cross sections and a detailed mapping of the five operator coefficients onto on-peak and off-peak observables, showing that off-shell data greatly enhances sensitivity to non-SM tensor structures, especially for the usually neglected $\mathcal{O}_4$ and $\mathcal{O}_5$ operators, while addressing potential unitarity issues via form factors or energy cutoffs. The paper demonstrates that on-peak measurements alone are insufficient to fully constrain the operator space and that off-shell measurements yield complementary information, with quantitative estimates of required luminosity for 3$\sigma$ exclusions. It also discusses the practical challenges of distinguishing certain operators on-peak and the need to account for interference with the $gg\to ZZ$ background in a full analysis. Overall, the results strengthen the case for a comprehensive, multi-kinematic strategy to pin down the tensor structure of the Higgs couplings to $Z$ bosons.

Abstract

We extend the study of Higgs boson couplings in the "golden" $gg\to H \to ZZ^\ast \to 4\ell$ channel in two important respects. First, we demonstrate the importance of off-shell Higgs boson production ($gg\to H^\ast \to ZZ \to 4\ell$) in determining which operators contribute to the $HZZ$ vertex. Second, we include the five operators of lowest non-trivial dimension, including the $Z_μZ^μ\Box H$ and $H Z_μ\Box Z^μ$ operators that are often neglected. We point out that the former operator can be severely constrained by the measurement of the off-shell $H^\ast \to ZZ$ rate and/or unitarity considerations. We provide analytic expressions for the off-peak cross-sections in the presence of these five operators. On-shell, the $Z_μZ^μ\Box H$ operator is indistinguishable from its Standard Model counterpart $H Z_μZ^μ$, while the $H Z_μ\Box Z^μ$ operator can be probed, in particular, by the $Z^\ast$ invariant mass distribution.

Figures (10)

• Figure 1: The distribution of the quantity $(M_{Z_1}^2 + M_{Z_2}^2)^2/ M_Z^4$, which is the ratio of differential cross sections due to the operator $\mathcal{O}_5$ and due to the SM operator, $\mathcal{O}_1$, as evaluated for SM events (see Eqs. (\ref{['Tim']}) and (\ref{['Tebow']})). The mean of this quantity is equal to $\gamma_{55}$.
• Figure 2: The differential cross section as a function of four-lepton invariant mass for $2e2\mu$ events before event selections. Results are shown for pure $\mathcal{O}_1$, $\mathcal{O}_2$, $\mathcal{O}_3$, $\mathcal{O}_4$, and $\mathcal{O}_5$ couplings (cf. Eq. (\ref{['Lag']})), as well as for the irreducible $q\bar{q} \to ZZ \to 2e2\mu$ background (bg). There is no event selection applied to the signal events; for the background, a minimal $M_{l\bar{l}} > 1$ GeV selection is applied to avoid infrared divergences. For each signal hypothesis, the normalization has been chosen to be equal to the entire SM on-peak Higgs boson cross section in this channel. In this figure, the $ggX$ coupling is taken to be constant with respect to invariant mass.
• Figure 3: The same as Fig. \ref{['fig:2e2mu-xsec-ggX-fixed']}, but in this figure, the $ggX$ coupling evolves with invariant mass according to the expression in Eq. (\ref{['ggH-evolve']}).
• Figure 4: The distribution of $Z$ invariant mass for the $Z$ with invariant mass closest to $M_Z$ ($M_{\rm ON}$, left) and the $Z$ with invariant mass furthest from $M_Z$ ($M_{\rm OFF}$, right), in $gg \to X \to ZZ \to 2e 2\mu$ events with $\hat{s} = 2$ TeV. The curve labeled "$\kappa_i \ne 0$" is the distribution for which $\kappa_i$ is non-vanishing but $\kappa_j = 0$ for $i\ne j$; these curves have the same colors as the corresponding curves in Figs. \ref{['fig:2e2mu-xsec-ggX-fixed']} and \ref{['fig:2e2mu-xsec-ggX-evolve']}. We learn that a significant fraction of events from $\mathcal{O}_5$, and to a lesser extent $\mathcal{O}_2$, involve very off-shell $Z$ bosons.
• Figure 5: The ratio between the actual partonic $gg \to ZZ^\ast \to 2e 2\mu$ cross section for pure $\mathcal{O}_5$ couplings, and the value of this partonic cross section calculated in Eq. (\ref{['os-analytic-integrated']}) using the narrow width approximation (NWA).