The geometric νSMEFT: operators and connections

Abstract

We write down a geometric realization of the Standard Model Effective Field Theory (SMEFT) extended by nf flavours of light sterile neutrinos, a so-called geoνSMEFT. As with the geoSMEFT introduced by Helset, Martin and Trott, we show that a refactorization of the νSMEFT’s operator product expansion is possible, such that two- and three-point composite operator forms are dressed with field-space connections composed of towers of Higgs dressings and symmetry generators, valid at all-orders in the {overline{v}}_T/Lambda expansion parameter of the EFT left({overline{v}}_Tequiv sqrt{2leftlangle {H}^{dagger }Hrightrangle}right) . These connections are parameterized by real Higgs coordinates and contribute to the field-space geometry of the (ν)SMEFT, with structure linked to the strength of Beyond-the-(ν)Standard Model physics encoded in {overline{v}}_T/Lambda . In addition to enumerating the relevant composite operators and associated connections, we briefly outline the route to calculating all- {overline{v}}_T/Lambda -orders amplitudes, including the flavor-invariant theory required to understand the neutrino mass-eigenstate basis geometrically.