Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching

TL;DR

This paper classifies gauge-invariant operators below the electroweak scale, computes their matching from SMEFT at tree level, and provides tools to connect low-energy measurements with high-energy new physics constraints.

Contribution

It provides a comprehensive classification of operators and the tree-level matching from SMEFT, enabling consistent analysis of low-energy effects of new physics.

Findings

Classified 70 dimension-five and 3631 dimension-six operators.

Computed tree-level matching from SMEFT to low-energy operators.

Facilitates combined analysis of low-energy experiments and LHC data.

Abstract

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $\Delta B= \pm \Delta L = \pm 1$, $\Delta L=\pm 2$, and $\Delta L=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/\Lambda^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.