# Matching for FCNC effects in the flavour-symmetric SMEFT

## TL;DR

This paper provides a comprehensive calculation of how the Standard Model Effective Field Theory with flavour symmetry matches onto the Weak Effective Theory, enabling precise analysis of flavour-changing neutral current effects.

## Contribution

It offers the first complete tree and one-loop matching of SMEFT with unbroken $U(3)^5$ flavour symmetry to WET operators, including corrections to input observables.

## Key findings

- Complete tree and one-loop matching formulas derived.
- Explicit calculation of SMEFT corrections to input observables.
- Facilitates high-precision flavour data integration into SMEFT fits.

## Abstract

We calculate the complete tree and one-loop matching of the dimension 6 Standard Model Effective Field Theory (SMEFT) with unbroken $U(3)^5$ flavour symmetry to the operators of the Weak Effective Theory (WET) which are responsible for flavour changing neutral current effects among down-type quarks. We also explicitly calculate the effects of SMEFT corrections to input observables on the WET Wilson coefficients, a necessary step on the way to a well-defined, complete prediction. These results will enable high-precision flavour data to be incorporated into global fits of the SMEFT at high energies, where the flavour symmetry assumption is widespread.