SMEFT interpretation of $\Delta$F = 2 transitions

TL;DR

This paper provides a comprehensive, model-independent analysis of $$F=2 transitions within the SMEFT framework, deriving master formulas for mixing amplitudes that incorporate renormalization effects and basis choices.

Contribution

It introduces two master formulas for BSM contributions to mixing amplitudes in SMEFT, accounting for renormalization group evolution and basis dependence, advancing the theoretical understanding of flavor transitions.

Findings

Derived master formulas for $M_{12}$ in terms of Wilson coefficients.

Highlighted the impact of renormalization group evolution from the top Yukawa coupling.

Showed the dependence of results on the choice of down or up basis in SMEFT.

Abstract

A model-independent anatomy of $\Delta F= 2$ transitions in the context of the Weak Effective Theory (WET) below the electroweak scale (EW) and the Standard Model Effective Field Theory (SMEFT) above the EW scale is discussed. Two master formulae for the BSM contribution of the mixing amplitude $M_{12}$, in terms of Wilson coefficients are presented. The coefficients entering these formulae contain all the information below the EW scale and the NP scale $\Lambda$, respectively. The renormalization group evolution from the top-quark Yukawa coupling has the largest impact on the result. The obtained expressions depend on whether the down-basis or the up-basis for SMEFT operators is considered.