Dirac Masses and Mixings in the (geo)SM(EFT) and Beyond

TL;DR

This paper provides exact, basis-independent formulas for calculating Dirac masses, mixings, and CP-violation parameters from Yukawa matrices within the SMEFT and geoSMEFT frameworks, applicable at all orders and to various flavor models.

Contribution

It introduces a complete, basis-independent formalism for Dirac flavor parameters in SMEFT and geoSMEFT, including RG flow expressions at all orders.

Findings

Exact formulas for Dirac masses and mixings derived

Formalism applies to models with different flavor dynamics

RG flow expressions for quark parameters obtained

Abstract

We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3$\times$3 Yukawa matrices $Y$ valid when $Y Y^\dagger \rightarrow U^\dagger \,Y Y^\dagger \, U$ under global $U(3)_{Q_L}$ flavour symmetry transformations $U$. The results apply to the Standard Model Effective Field Theory (SMEFT) and its `geometric' realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the $\sqrt{2 \langle H^\dagger H \rangle} / \Lambda$ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism's utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.