On The Potential of Minimal Flavour Violation

TL;DR

This paper explores the scalar potential under the Minimal Flavour Violation hypothesis, analyzing how different operator dimensions influence quark mass hierarchies and mixing angles, with implications for flavor physics models.

Contribution

It derives the scalar potential for Yukawa fields within the MFV framework and compares effects of dimension five and six operators on flavor structure.

Findings

Dimension five operators do not induce mixing.

Dimension six operators generate a mixing angle.

Mass hierarchies are naturally produced by dimension six operators.

Abstract

Assuming the Minimal Flavour Violation hypothesis, we derive the general scalar potential for fields whose background values are the Yukawa couplings. We analyze the minimum of the potential and discuss the fine-tuning required to dynamically generate the mass hierarchies and the mixings between different quark generations. Two main cases are considered, corresponding to Yukawa interactions being effective operators of dimension five or six (or, equivalently, resulting from bi-fundamental and fundamental scalar fields, respectively). At the renormalizable and classical level, no mixing is naturally induced from dimension five Yukawa operators. On the contrary, from dimension six Yukawa operators one mixing angle and a strong mass hierarchy among the generations result.