Renormalization-group running of dimension-8 four-fermion operators in the SMEFT

TL;DR

This paper calculates how dimension-8 four-fermion operators in SMEFT evolve with energy scale, revealing significant effects at low energies but minimal impact on LHC Drell-Yan data analysis.

Contribution

It provides the first detailed analytic and numerical study of the renormalization-group evolution of dimension-8 four-fermion operators in SMEFT, including flavor structures.

Findings

Running effects can reach 50% from 10 TeV to GeV scales.

Dimension-8 running has minimal impact on LHC Drell-Yan data analysis.

Analytic results for flavor structures are presented.

Abstract

We compute the renormalization-group equations governing the evolution of dimension-8 four-fermion operators in the Standard Model Effective Field Theory (SMEFT). We describe the calculation and present analytic results for both the full flavor structure of the SMEFT and with the assumption of minimal flavor violation. We present numerical results for the renormalization-group evolution of the coefficients, and study their impact on fits of the Large Hadron Collider (LHC) Drell-Yan data. The effects of running on the dimension-8 coefficients can reach 50\% or more when evolving from 10 TeV scale down to few-GeV energies relevant for the analysis of fixed-target data. However, the impact of the dimension-8 running on the analysis of Drell-Yan data from the LHC is minimal.