Minimal Flavour Violation

TL;DR

This paper discusses models with minimal flavour violation (MFV), focusing on their parametrization, potential new physics contributions, and implications for B and K meson decays, including a specific model with extra dimensions.

Contribution

It provides a framework to analyze MFV models using master functions, highlighting correlations between observables and proposing strategies for their determination.

Findings

MFV models can be described with 11 parameters, including CKM parameters and master functions.

Only 4 or 5 master functions are likely to receive significant new physics contributions.

Relations between observables that do not depend on master functions are identified.

Abstract

These lectures give a description of models with minimal flavour violation (MFV) that can be tested in $B$ and $K$ meson decays. This class of models can be formulated to a very good approximation in terms of 11 parameters: 4 parameters of the CKM matrix and 7 values of the {\it universal} master functions $F_r$ that parametrize the short distance contributions. In a given MFV model, $F_r$ can be calculated in perturbation theory and are generally correlated with each other but in a model independent analysis they must be considered as free parameters. We conjecture that only 5 or even only 4 of these functions receive significant new physics contributions. We summarize the status of the CKM matrix, outline strategies for the determination of the values of $F_r$ and present a number of relations between physical observables that do not depend on $F_r$ at all. We emphasize that the formulation of MFV in terms of master functions allows to study transparently correlations between $B$ and $K$ decays which is very difficult if Wilson coefficients normalized at low energy scales are used instead. We discuss briefly a specific MFV model: the Standard Model with one universal large extra dimension.