Renormalization Group Evolution of Flavour Invariants

TL;DR

This paper develops a basis-independent framework using flavour invariants to analyze the renormalization-group evolution of fermion masses and mixings in the Standard Model, highlighting hierarchical simplifications.

Contribution

It constructs a complete set of flavour invariants and derives their RG equations, incorporating hierarchy-based simplifications in the SM and minimal-flavour violating models.

Findings

Constructed a basis-independent set of flavour invariants.

Derived RG equations for these invariants.

Identified hierarchy-based simplifications in the RG analysis.

Abstract

The fermion spectrum in the Standard Model (SM) exhibits hierarchical structures between the eigenvalues of the Yukawa matrices which determine the fermion masses, as well as certain hierarchical patterns in the mixing matrix that describes weak transitions between different fermion generations. A basis-independent description of the SM flavour structure can be given in terms of a complete set of flavour invariants. In this paper, we construct a convenient set of such invariants, and discuss the general form of the renormalization-group equations. We also discuss the simplifications that arise from exploiting hierarchies in Yukwawa couplings and mixings which are present in the SM or its minimal-flavour violating extensions.