Scale-independent relations between neutrino mass parameters

TL;DR

The paper tackles whether scale-independent relations among neutrino mass parameters can survive quantum corrections when SUSY is absent, by focusing on invariants $I_{fg}$ constructed from the Weinberg operator. It derives the RG evolution of these invariants, showing they are RG-invariant at 1-loop and acquire only tiny two-loop corrections of the form $\dot I_{fg} = \frac{2\,(y_f^2 - y_g^2)^2}{(16\pi^2)^2} I_{fg}$. Consequently, for the SM and 2HDM, the $I_{fg}$ remain effectively constant across the flavor scale, allowing modular-flavor predictions to be confronted with data without detailed RG analysis. This provides a practical bridge between UV flavor symmetries and experimental observables, enabling direct probes of high-scale physics from measured neutrino parameters.

Abstract

Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and holomorphicity. We find that even in the absence of supersymmetry these combinations are surprisingly immune against quantum corrections.