The geometric νSMEFT: operators and connections

Abstract

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 $$ {\overline{v}}_T/\Lambda $$ v ¯ T / Λ expansion parameter of the EFT $$ \left({\overline{v}}_T\equiv \sqrt{2\left\langle {H}^{\dagger }H\right\rangle}\right) $$ v ¯ T ≡ 2 H † H . 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 $$ {\overline{v}}_T/\Lambda $$ v ¯ T / Λ . In addition to enumerating the relevant composite operators and associated connections, we briefly outline the route to calculating all-$$ {\overline{v}}_T/\Lambda $$ v ¯ T / Λ -orders amplitudes, including the flavor-invariant theory required to understand the neutrino mass-eigenstate basis geometrically.