On the Validity of the Effective Field Theory Approach to SM Precision Tests

TL;DR

This paper analyzes when the Standard Model EFT extended by dimension-6 operators provides a faithful low-energy description of UV theories and how to quantify the validity range of truncating at $D=6$. It advocates reporting experimental constraints as functions of the process energy scale $M_{\rm cut}$ to retain broad UV interpretability, and develops a practical power-counting framework with a single scale $\Lambda$ and coupling $g_*$ to relate $c_i^{(6)}$ to UV parameters and to gauge when $D=8$ operators or loop corrections become relevant. The authors highlight that $D=8$ effects can dominate in special symmetry-driven or fine-tuned scenarios, that loop and real-emission corrections can be numerically important for precise observables, and demonstrate these ideas with a concrete vector-triplet UV model. Their guidance provides both conceptual clarity and actionable prescriptions for robust EFT analyses of SM precision tests at colliders, enabling more reliable connections between experimental results and possible UV completions.

Abstract

We discuss the conditions for an effective field theory (EFT) to give an adequate low-energy description of an underlying physics beyond the Standard Model (SM). Starting from the EFT where the SM is extended by dimension-6 operators, experimental data can be used without further assumptions to measure (or set limits on) the EFT parameters. The interpretation of these results requires instead a set of broad assumptions (e.g. power counting rules) on the UV dynamics. This allows one to establish, in a bottom-up approach, the validity range of the EFT description, and to assess the error associated with the truncation of the EFT series. We give a practical prescription on how experimental results could be reported, so that they admit a maximally broad range of theoretical interpretations. Namely, the experimental constraints on dimension-6 operators should be reported as functions of the kinematic variables that set the relevant energy scale of the studied process. This is especially important for hadron collider experiments where collisions probe a wide range of energy scales.

Figures (2)

• Figure 1: Left: The partonic $u \bar{d} \to W^+ h$ cross section as a function of the center-of-mass energy of the parton collision. The black lines correspond to the $SU(2)_L$ triplet model with $M_V =1\,$TeV, $g_H=-g_q = 0.25$ (dashed), $M_V = 2\,$TeV, $g_H=-g_q = 0.5$ (dotted), and $M_V = 7\,$TeV, and $g_H=-g_q = 1.75$ (solid). The corresponding EFT predictions are shown in the linear approximation (solid red), and when quadratic terms in $D\!=\!6$ parameters are included in the calculation of the cross section (solid purple). Right: Theory error as a function of $M_V$ (solid line). The error is defined to be the relative difference between the constraints on $g_*^2 \equiv g_H^2 = g_q^2$ obtained by recasting the limits derived in the framework of a $D\!=\!6$ EFT and those derived from the resonance model. The limits come from re-interpreting the hypothetical experimental constraints with $M_{\rm cut} = 3\,$TeV, as described in the text. The dotted line corresponds to the naive estimate $(M_{\rm cut}/M_V)^2$.
• Figure 2: Limits on the coupling strength $g_* \equiv - g_H = g_q$ as a function of the resonance mass $M_V$. The solid and dashed red curves are obtained respectively from the vector resonance model and a naive analysis in terms of a $D$=6 truncated EFT, including data from all energies. The dark (light) blue region corresponds instead to the bound derived from a consistent EFT analysis where only data with $M_{Wh}<M_{\rm cut}=\kappa M_V$ are used with $\kappa$=0.5 (1).