Low-energy effective field theory below the electroweak scale: operators and matching

Abstract

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 ΔB = ±ΔL = ±1, ΔL = ±2, and ΔL = ±4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ2 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.