Exact One-Loop Evolution Invariants in the Standard Model

TL;DR

This paper constructs exact renormalisation group invariants in the Standard Model that connect quark masses and mixing parameters, offering new insights into the flavor structure and potential implications for particle physics.

Contribution

It introduces a set of exact SM invariants linking quark masses and mixing, revealing a unique Yukawa matrix combination and extending to leptons with Dirac neutrinos.

Findings

Identifies a simple Yukawa matrix combination with significant role in the SM.

Constructs exact RG invariants relating quark masses and mixing parameters.

Suggests potential new insights into the flavor spectrum of quarks.

Abstract

Guided by considerations of flavour symmetry, we construct a set of exact Standard Model (SM) renormalisation group evolution invariants which link quark masses and mixing parameters. We examine their phenomenological implications and infer a simple combination of Yukawa coupling matrices which plays a unique role in the SM, suggesting a possible new insight into the observed spectrum of quark masses. Our evolution invariants are readily generalised to the leptons in the case of Dirac neutrinos, but do not appear to be relevant for either quarks or leptons in the MSSM.