Fermion Geometry and the Renormalization of the Standard Model Effective Field Theory

TL;DR

This paper develops a geometric framework for fermions in effective field theories, simplifying quantum loop calculations and deriving fermion contributions to the renormalization group equations in the Standard Model EFT.

Contribution

It extends the geometric description of field space to include fermions, enabling more efficient computation of loop corrections in EFTs.

Findings

Derived fermion loop contributions to RG equations up to dimension eight.

Reorganized quantum corrections using geometric methods.

Simplified calculations of fermionic effects in the Standard Model EFT.

Abstract

The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.