The generic basis and flavour non-universal SMEFT

TL;DR

This paper advocates for using a generic weak basis in SMEFT analyses of flavour anomalies, enabling direct inclusion of transformation matrices and potential reconstruction of Yukawa matrices, thus providing a more comprehensive understanding of flavour physics.

Contribution

It introduces a framework that incorporates the transformation matrices explicitly in SMEFT analyses, moving beyond traditional basis assumptions.

Findings

Allows direct determination of transformation matrices from data

Enables potential reconstruction of Yukawa matrices

Provides a more general approach to flavour anomaly analysis

Abstract

Whenever an anomaly in the flavour sector appears, analyses are performed examining whether it can be explained by adding a small number of carefully-chosen flavour non-universal four-fermion SMEFT operators. These analyses are typically carried out in the down or the up basis, i.e., it is assumed that the weak and mass eigenstates are the same for the left-handed down-type or up-type quarks. In these bases, there is no dependence on the matrices that transform from the weak to the mass basis, and which are unmeasurable in the Standard Model. In this paper, we argue that it is better to use a generic weak basis, in which no assumptions about the alignment of weak and mass eigenstates are made. The analysis now directly includes elements of the transformation matrices. By doing a fit to the data, it is possible to both determine if the flavour anomaly can be explained and extract the transformation matrices. In principle, this can be extended to a complete reconstruction of the Yukawa matrices.