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

Understand

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.