Limitations and Opportunities of Off-Shell Coupling Measurements

TL;DR

The paper critically examines off-shell Higgs width constraints, arguing that interpreting off-shell cross sections as a bound on $Γ_h$ relies on strong model-specific assumptions and can be invalidated by various BSM scenarios. It analyzes unitarity constraints, presents explicit BSM counterexamples (a Higgs-portal scalar and vector-like quarks) that decorrelate on- and off-shell regions, and discusses how higher-dimensional operators can enhance CP sensitivity using off-shell data. It also proposes a more model-independent route via weak-boson-fusion off-shell measurements, albeit with significantly reduced rates, and notes that a precise, model-independent width determination may ultimately require future lepton colliders. Overall, the work reframes off-shell Higgs measurements as tools for CP tests and EFT investigations rather than guarantees of a universal width bound.

Abstract

Indirect constraints on the total Higgs width $Γ_h$ from correlating Higgs signal strengths with cross section measurements in the off-shell region for $p(g)p(g)\to 4\ell$ production have received considerable attention recently, and the CMS collaboration have published a first measurement. We revisit this analysis from a new physics and unitarity constraints perspective and conclude that limits on $Γ_h$ obtained in this fashion are not reliable unless we make model-specific assumptions, which cannot be justified at the current stage of the LHC programme. Relaxing the $Γ_h$ interpretation, we discuss the merits of high invariant mass cross section measurements in the context of Higgs CP analyses, higher dimensional operator testing, and resolved new physics in the light of electroweak precision constraints beyond effective theory limitations. Furthermore, we show that a rather model-independent LHC constraint can be obtained from adapting the $gg\to 4\ell$ analysis to the weak boson fusion channels at lower statistical yield.

Figures (9)

• Figure 1: Constraining the total Higgs width by fixing the signal strength (on-shell region) and measuring the cross section at large invariant $ZZ$ masses, keeping couplings in the on-shell and Higgs off-shell region fixed. Distributions are leading order, while keeping all quarks dynamical and the bottom and top quarks massive. We have chosen a minimal cut set $p_{T}(\ell)\geq 10~\text{GeV}$, $|y(\ell)|\leq 2.5$, $\Delta R(\ell\ell')\geq 0.4$.
• Figure 2: Representative Feynman diagram topologies contributing to $gg\to ZZ$ with leptonic $Z$ boson decays in the SM and theories with extended fermionic sectors.
• Figure 3: Individual leading order contributions from Fig. \ref{['fig:feyzz']} to the full hadronic cross section. For comparison we also include the effective theory distribution resulting from a $ggh$ effective vertex in the $m_t\to \infty$ limit. Cuts are identical to Fig. \ref{['fig:zzsm']}. The coloured scalars are for representative values of $\lambda$ and $\Gamma_h$ to illustrate their behaviour. For additional details see text.
• Figure 4: Unpolarized $t\bar{t} \to ZZ$ cross section as function of energy. We demonstrate unitarity cancellations between the gauge and Yukawa-type interactions (blue solid and dashed; the dashed line lies on top of the solid line), yielding a well-defined SM cross section (orange). We also show the parameter choice that corresponds to the CMS-like exclusion of $\Gamma_h \simeq 5 \times \Gamma_{h}^{\mathrm{SM}}$ based on the strategy outlined in hcms and the introduction.
• Figure 5: Zeroth partial wave projection for $gg\to Z_L Z_L$ for the SM and various values of the $g_{ggh}g_{ZZh}$-rescaling as a consequence of $\mu=1$ and $\Gamma_h>\Gamma_h^{\text{SM}}$. We also show the partial wave projection for longitudinal $WW$ scattering in the SM with and without Higgs to put $gg\to ZZ$ into context.