[Paper Review] The Standard Model effective field theory at work

Gino Isidori, Felix Wilsch+1 more|arXiv (Cornell University)|Mar 29, 2023

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a comprehensive review of the Standard Model Effective Field Theory (SMEFT) as a systematic framework to explore physics beyond the Standard Model. It details the construction of SMEFT, including operator basis choices, matching procedures, and renormalization group evolution, demonstrating its application to low-energy and high-pT phenomenology with explicit examples.

ABSTRACT

The striking success of the Standard Model in explaining precision data and, at the same time, its lack of explanations for various fundamental phenomena, such as dark matter or the baryon asymmetry of the universe, suggests new physics at an energy scale much larger than the electroweak scale. In the absence of a short-range-long-range conspiracy, the Standard Model can be viewed as the leading term of an effective "remnant" theory (referred to as the SMEFT) of a more fundamental structure. Over the last years, many aspects of the SMEFT have been investigated and it has become a standard tool to analyze experimental results in an integral way. In this article, after briefly presenting the salient features of the Standard Model, we review the construction of the SMEFT. We discuss the range of its applicability and bounds on its coefficients imposed by general theoretical considerations. Since new physics models are likely to exhibit exact or approximate accidental global symmetries, especially in the flavor sector, we also discuss their implications for the SMEFT. The main focus of our review is the phenomenological analysis of experimental results. We show explicitly how to use various effective field theories to study the phenomenology of theories beyond the Standard Model. We give a detailed description of the matching procedure and the use of the renormalization group equations, allowing to connect multiple effective theories valid at different energy scales. Explicit examples from low-energy experiments and from high-$p_T$ physics illustrate the workflow. We also comment on the non-linear realization of the electroweak symmetry breaking and its phenomenological implications.

Motivation & Objective

• To establish SMEFT as a systematic and consistent framework for describing new physics at energy scales above the electroweak scale.
• To clarify the construction of the SMEFT operator basis, including the Warsaw basis and treatment of evanescent operators.
• To analyze theoretical constraints on SMEFT coefficients, such as unitarity, positivity, and gauge anomaly cancellation.
• To demonstrate the matching of UV-complete BSM models to SMEFT and the use of renormalization group equations to connect different energy scales.
• To illustrate the phenomenological use of SMEFT in low-energy and high-pT experiments, including global fits and Drell-Yan tails.

Proposed method

• Use of the Warsaw basis to construct a non-redundant set of higher-dimensional operators in SMEFT, ensuring completeness and minimality.
• Application of dimensional regularization with the (semi-)naïve dimensional regularization (NDR) scheme for handling γ₅ in D dimensions, including consistent treatment of trace ambiguities.
• Employment of the method of regions to separate UV and IR divergences, enabling automatic renormalization of the EFT and extraction of RG equations.
• Implementation of diagrammatic and functional matching techniques to relate UV models to SMEFT at the weak scale.
• Use of renormalization group evolution to run SMEFT coefficients from the weak scale down to low energies, connecting to the Low-Energy Effective Theory (LEFT).
• Analysis of non-linear realizations of electroweak symmetry breaking via the Higgs Effective Field Theory (HEFT) and geometric formulations of the scalar sector.

Figure 1: Pulls of the electroweak observables as obtained by a global SM fit, namely differences between SM predictions and direct measurements, normalized to the experimental uncertainties. From [ 218 ] see also [ 217 ] .

Experimental results

Research questions

• RQ1 How can the SMEFT be systematically constructed as an effective field theory valid below the new physics scale?
• RQ2 What are the theoretical constraints—such as unitarity, positivity, and gauge anomalies—that limit the allowed values of SMEFT Wilson coefficients?
• RQ3 How do accidental global symmetries, such as flavor symmetries or custodial symmetry, constrain SMEFT operators and their running?
• RQ4 What is the correct procedure for matching a UV BSM model to SMEFT, and how can the resulting SMEFT be evolved via RG equations?
• RQ5 How can SMEFT be used to interpret experimental data from low-energy processes and high-pT collider searches, including global fits?

Key findings

• The SMEFT in the Warsaw basis provides a non-redundant, complete, and gauge-invariant framework for describing new physics at energy scales above the electroweak scale.
• The method of regions allows for a clean separation of UV and IR divergences, ensuring automatic renormalization of the EFT and simplifying the derivation of RG equations.
• Evanescent operators contribute to the RG evolution and physical amplitudes, and their effects are fully encoded in the UV region of the method of regions.
• The NDR scheme for γ₅ in dimensional regularization is sufficient for the purposes of this review, though it introduces reading-point ambiguities in traces with an odd number of γ₅ matrices.
• Matching BSM models to SMEFT via diagrammatic and functional methods enables a consistent connection between UV theories and low-energy observables.
• Global fits using SMEFT at high-pT, such as in Drell-Yan tails, show sensitivity to new physics beyond the SM, with constraints on SMEFT coefficients derived from experimental data.

Figure 3: The Feynman diagram on the left-hand side shows a process in the UV theory generating the effective four-fermion operator shown on the right-hand side. The solid lines represent SM fermions, whereas the dashed line denotes a heavy bosons (either vector or scalar).