Vices and Virtues of Higgs EFTs at Large Energy

TL;DR

The paper examines the use of Higgs effective field theories with dimension-6 operators to constrain heavy new physics, focusing on HV associated production where high-energy behavior is sensitive to energy-growing operators. It emphasizes that naive EFT applications can break down in the high-energy tail, but under specific UV completions—particularly with a strongly coupled composite fermion sector—the combination ${\cal O}_W-{\cal O}_B$ can yield meaningful, high-energy constraints that complement LEP1 and compete with LEP2 bounds. By analyzing ATLAS Higgs searches in $pp\to Zh$ and $pp\to W h$ with $h\to b\bar b$, the authors extract differential bounds on the relevant Wilson coefficients and show that EFT validity severely restricts the regions where robust conclusions can be drawn, except in the composite-fermion scenario. They also compare with Triple Gauge Couplings measurements, illustrating that Higgs-based probes access largely orthogonal directions in parameter space, and highlight the importance of UV completions and unitarity considerations for interpreting high-energy EFT limits in current and future LHC data.

Abstract

We study constraints on new physics from Higgs production at the LHC in the context of an effective field theory (EFT), focusing on Higgs searches in $HV$ ($V=W,Z$) associated production which are particularly sensitive to the high-energy behavior of certain dimension-6 operators. We show that analyses of these searches are generally dominated by a kinematic region where the generic EFT expansion breaks down, and establish under which conditions they can nevertheless be meaningful. For example, constraints from these searches on the Wilson coefficients of operators whose effects grow with energy can be established in scenarios where a particular combination of fermions and the Higgs are composite and strongly coupled: then, bounds from Higgs physics at high energy are complementary to LEP1 and competitive with LEP2.

Figures (5)

• Figure 1: To illustrate the UV behavior of the operators $\mathcal{O}_{V}$, these plots contrast the partonic LO distributions of $p_T(V)$ and $\Delta R(b,\overline b)$ ($pp\rightarrow ZH$@8TeV) for the SM and SM+$\mathcal{O}_{V}$ with large Wilson coefficients.
• Figure 2: The impact of the operators $\mathcal{O}_{WW}$ and $\mathcal{O}_{W}$ on the cross section and kinematics of $pp\rightarrow Wh$ at the LHC8. Shown is $\sigma/\sigma_{SM}$ (LEFT) and $\sigma/\sigma_{SM}(p_T>200)$ (RIGHT). The net effect of $\mathcal{O}_{WW}$ on the signal strength is subdominant in the region $p_T(W)>200$ GeV. We assume that the EFT is valid up to the unitarity cutoff.
• Figure 3: The $c_{W}$ dependence of the $u\overline d \rightarrow hW^+$ cross section at different fixed c.o.m. energies $\sqrt{\hat{s}} =400,500,1200$ as described in the text. All orders of $c_{W}$ are included in the squared amplitude for the solid lines. The dashed lines represent the linearized signal strengths.
• Figure 4: The combined expected (LEFT) and observed (RIGHT) 1-parameter fit $\Delta \chi^2$ contours in the coefficient $c_{W}(m_W^2/\Lambda^2)=-c_{B}(m_W^2/\Lambda^2)$ from Higgs searches in the $b\overline b+0l,1l,2l$ final states in ATLAS. We assume all other operators in the basis to be negligible and employ various UV cutoff prescriptions. The dashed contours are for fixed UV cuts $\sqrt{\hat{s}} < 500,550,\dots$ GeV, while the solid contours are for parameter-dependent cutoffs $\hat{s}< \Lambda^2/c_W$ (blue), $2 \Lambda^2/c_W$ (purple), $4 \Lambda^2/c_W$ (yellow) and $4 \pi\,\Lambda^2/c_W$ (green) inspired by our discussion of UV completions and perturbativity. We assume that the main source of error is systematic, and treat the theoretical errors as nuisances.
• Figure 5: The $95CL$ (solid) and $99CL$ (dashed) combined observed limits on the coefficients $c_{W}$ and $c_{\overline{HB}}$ (with $c_B=-c_W$ and all other operators set to zero) from our analysis of Higgs searches in the $b\overline b+0l,1l,2l$ final states in ATLAS. We employ a cut $\sqrt{\hat{s}}<1.2$ TeV. We compare the exclusion with LEP2 limits on TGCs (red contour).