A Complete Set of the Dimension-8 Green's Basis Operators in the Standard Model Effective Field Theory

TL;DR

This paper constructs a complete, systematic off-shell Green's basis of dimension-8 operators in the Standard Model EFT, enabling explicit removal of redundancies and facilitating future EFT analyses.

Contribution

It introduces an off-shell amplitude formalism that uniquely maps to operators, allowing systematic redundancy removal and comprehensive basis construction at dimension 8.

Findings

993+1649 independent operators for one generation

44807+66197 operators for three generations

Method applicable to any EFT at arbitrary mass dimension

Abstract

We present a complete and independent off-shell Green's basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We propose an off-shell amplitude formalism such that this new kind of amplitudes has a one-to-one correspondence to general operators carrying all kinds of redundancies. The advantage of such formalism is that all kinds of redundancies can be formulated explicitly in terms of the off-shell spinors and thus be removed systematically from the exhaustive list of the general off-shell amplitudes. Following such procedure, redundant operators can be reduced to the ones with the only redundancy from the equation of motion kept, the Green's basis. We find there are (993+1649) independent (on-shell + off-shell) operators for one generation of fermions and (44807+66197) ones for three generations at the dimension 8. This systematic method can be applied to obtain the Green's basis at any mass dimension for general EFTs.