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

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 = +/-Delta L 1, Delta L = +/- 2, and Delta L = +/- 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.