Renormalization Invariants and Quark Flavor Mixings

TL;DR

This paper constructs renormalization invariants linking quark flavor mixings and mass ratios, explaining empirical relations through renormalization evolution in various electroweak models.

Contribution

It introduces approximate analytical solutions for RGEs that reveal explicit correlations between quark mixings and mass ratios across different models.

Findings

Invariants explain empirical relations like θ23 ∝ m_s/m_b and θ13 ∝ m_d/m_b.

Numerical solutions confirm the invariants' validity up to the GUT scale.

Scale dependence of mixing angles closely follows the invariants.

Abstract

A set of renormalization invariants is constructed using approximate, two-flavor, analytic solutions for RGEs. These invariants exhibit explicitly the correlation between quark flavor mixings and mass ratios in the context of the SM, DHM and MSSM of electroweak interaction. The well known empirical relations $\theta_{23}\propto m_s /m_b $, $\theta_{13}\propto m_d /m_b$ can thus be understood as the result of renormalization evolution toward the infrared point. The validity of this approximation is evaluated by comparing the numerical solutions with the analytical approach. It is found that the scale dependence of these quantities for general three flavoring mixing follows closely these invariants up to the GUT scale.