Assessing (H)EFT theory errors by pitting EoM against Field Redefinitions

TL;DR

The paper addresses theoretical uncertainties arising from truncating HEFT EFTs in the Higgs sector and the interplay between field redefinitions and equation-of-motion reductions, with particular focus on the momentum-dependent operator $O_{\Box\Box}$. It compares three formulations—vanilla HEFT, field-redefined HEFT, and EoM-substituted Lagrangians—and derives how $O_{\Box\Box}$ modifies the Higgs propagator $G_h(p^2)$ and related amplitudes. On-shell Higgs observables yield consistent leading-order bounds across formulations, while off-shell and rare processes such as four-top production reveal larger truncation uncertainties due to momentum dependence. The study provides a data-driven framework to quantify EFT truncation error, connecting to power counting and unitarity constraints, and guiding SMEFT/HEFT interpretations at current and future colliders.

Abstract

Truncations of effective field theory expansions are technically necessary but inherently intertwined with the redundancies of general field redefinitions. This can be viewed as a juxtaposition of power-counting and theoretical uncertainties, which seek to estimate neglected higher-dimensional interactions through approaches based on community consensus. One can then understand the invariance of physics under field redefinitions as a data-informed validation of different power-counting schemes, or as a means of assigning theoretical errors in comparison with algebraic, equation of motion-based replacements. Such an approach generalises widely accepted procedures for estimating theoretical uncertainties within the SM to non-renormalisable interactions. We perform a case study for a representative example in Higgs Effective Field theory, focusing on universal Higgs properties tensioned against process-dependent sensitivity expectations.

Figures (6)

• Figure 1: Ratio of the BSM-modified to SM cross section for $gg \to h \to \gamma\gamma$ at $\sqrt{s} = 13~\text{TeV}$, as a function of $a_{\Box\Box}/v^2$. Theoretical variations corresponding to the vanilla HEFT model, field redefinition, and EoM reduction are shown. Shaded bands indicate current (LHC, integrated luminosity of $139~\text{fb}^{-1}$ATLAS:2022vkf) and projected (HL-LHC, integrated luminosity of $3~\text{ab}^{-1}$Cepeda:2019klc) experimental sensitivities at 95% CL. The lower panel shows the theory error calculated using Eq. (\ref{['eq:therr']}).
• Figure 2: The $\chi^2$ fit to $a_{\Box \Box}$ from Higgs signal strength data ATLAS:2022vkf (left), and the resulting extrapolation to the High Luminosity (HL-LHC) frontier (right, assuming a SM outcome) for the different HEFT Lagrangians described in the text. The $68\%$ and $95\%$ constraints are shown by the dotted and dashed black lines on the plots, respectively.
• Figure 3: Cross-section dependence of $p p \to t \bar{t} t \bar{t}$ at $\sqrt{s} = 13$ TeV with $a_{\Box \Box}$ for the vanilla and field redefined case for linear and quadratic truncations in the amplitudes. The light and dark bands in blue present the $95\%$ confidence limits in the current (at an integrated luminosity of $139~\text{fb}^{-1}$) and HL-LHC projected (at $3~\text{ab}^{-1}$) sensitivities to the 4-top signal strength. The lower panel illustrates the theory errors associated with the different parameterisations described previously.
• Figure 4: The four top invariant mass differential distributions for two benchmark points, including the SM, the linear and quadratic contributions from $a_{\Box \Box}$.
• Figure 5: Invariant $t\bar{t}$ mass distribution for $pp \to t \bar{t} t \bar{t}$ at $\sqrt{s}=13~\text{TeV}$ (including quadratic contributions from $a_{\Box \Box}$).