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Minimal Flavour Violation

Andrzej J. Buras

TL;DR

The paper presents Minimal Flavour Violation (MFV) as a framework in which all flavor-changing processes are CKM-driven, with short-distance physics captured by seven universal master functions $F_r(v)$ alongside four CKM parameters. It develops a model-independent master formula for decay amplitudes, $A = P_c + \sum_r P_r F_r(v)$, highlighting how $F_r(v)$ can be computed in specific models and how ratios of observables yield $F_r$-independent sum rules to test MFV. The CKM parameters are determined primarily from tree-level processes, while the remaining constraints from FCNC processes shape the Unitarity Triangle and the master-function values, enabling transparent B–K decay correlations. A reduced set of master functions is discussed to simplify phenomenology, and an explicit MFV model with a universal large extra dimension is examined as a concrete example. The work emphasizes the utility of the master-function formalism for connecting high-scale new physics with low-energy flavor observables.

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.

Minimal Flavour Violation

TL;DR

The paper presents Minimal Flavour Violation (MFV) as a framework in which all flavor-changing processes are CKM-driven, with short-distance physics captured by seven universal master functions alongside four CKM parameters. It develops a model-independent master formula for decay amplitudes, , highlighting how can be computed in specific models and how ratios of observables yield -independent sum rules to test MFV. The CKM parameters are determined primarily from tree-level processes, while the remaining constraints from FCNC processes shape the Unitarity Triangle and the master-function values, enabling transparent B–K decay correlations. A reduced set of master functions is discussed to simplify phenomenology, and an explicit MFV model with a universal large extra dimension is examined as a concrete example. The work emphasizes the utility of the master-function formalism for connecting high-scale new physics with low-energy flavor observables.

Abstract

These lectures give a description of models with minimal flavour violation (MFV) that can be tested in and 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 that parametrize the short distance contributions. In a given MFV model, 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 and present a number of relations between physical observables that do not depend on at all. We emphasize that the formulation of MFV in terms of master functions allows to study transparently correlations between and 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.

Paper Structure

This paper contains 15 sections, 56 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory of MFV
  3. Preface
  4. The Basis
  5. The Basic Idea
  6. CKM Matrix and the Unitarity Triangle (UT)
  7. Master Functions
  8. A Guide to the Literature
  9. Comments on QCD Corrections
  10. A Useful Conjecture: Reduced Set of Master Functions
  11. Summary
  12. Determination of the CKM Parameters
  13. The Determination of $|V_{us}|$, $|V_{ub}|$ and $|V_{cb}|$
  14. Completing the Determination of the CKM Matrix
  15. General Procedure in the SM

Figures (3)

  • Figure 1: Unitarity Triangle.
  • Figure 2: Typical Penguin and Box Diagrams in the SM.
  • Figure :