On-Shell Renormalization of Dim-8 SMEFT from Complete Amplitude Basis: I. Four-Fermion Operators

TL;DR

This paper derives the complete one-loop renormalization group equations for four-fermion operators at dimension-8 in SMEFT using an on-shell approach and Young Tensor basis, enabling systematic and comprehensive analysis.

Contribution

It introduces a novel on-shell framework with Young Tensor basis to compute dimension-8 SMEFT RGEs, including full flavor structures and a computational algorithm.

Findings

Derived full one-loop RGEs for dimension-8 four-fermion operators.

Implemented the method in the Mathematica package ABC4EFT.

Provided the complete RGE results as supplementary material.

Abstract

We compute the complete one-loop renormalization group equations (RGEs) for all the four-fermion operators at dimension-8 Standard Model Effective Field Theory (SMEFT). We adopt the on-shell framework, where the RGEs are obtained from the unitarity cuts of the bubble integrals. To construct a consistent set of RGEs without redundancy, we utilize the Young Tensor amplitude/operator basis as the building blocks of the tree-level amplitudes that constitute the unitarity cuts, which incorporates the full flavor structures of the effective operators. Due to the large number of effective operators for a dimension-8 type, it is crucial to reduce the integrated cuts to the same RGE amplitude basis, which is also made possible by the algorithm in the Young Tensor method. With the Mathematica package ABC4EFT that implements the method, we obtain the full result of the dimension-8 four-fermion RGEs with the output file attached as the supplementary material.