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 $$ {\overline{v}}_T/\Lambda $$ 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.

On amplitudes and field redefinitions

“…This makes the invariance of amplitudes under the restricted set of field redefinitions completely manifest. This approach has seen recent applications to the scalar sector of the Standard Model [64][65][66][67][68][69][70][71][72][73][74], and has also led to new insights into the properties of amplitudes for both scalars and particles of higher spins [75][76][77][78][79][80][81][82][83][84][85][86].…”