Renormalisation Group Invariants from Scaling and Non-overlapping Symmetries

TL;DR

This paper introduces a method to derive Renormalisation Group Invariants using scaling and non-overlapping symmetries, with applications to multi-scalar potentials and models like the two-Higgs doublet model.

Contribution

It presents a novel spurion-field approach for constructing RGIs that applies to complex scalar potentials and addresses the gauge-hierarchy problem.

Findings

Demonstrates the construction of RGIs for bilinear operators at all loops.

Applies the method to non-supersymmetric models including the two-Higgs doublet model.

Shows the relevance of scale-invariant directions in identifying RGIs.

Abstract

We show how the synergy of scaling and non-overlapping global symmetries can lead to Renormalisation Group Invariants (RGIs) among the parameters of potentials with multiple scalars. The instrumental role of scale-invariant field directions in the identification and construction of RGIs for bilinear field operators to all loops is demonstrated. We present a few illustrative examples to showcase our constructive spurion-field approach, which is applied to simple non-supersymmetric models as well as to scenarios reported recently in the literature that include the two-Higgs doublet model. The implications of our spurion-field formalism to address the gauge-hierarchy problem are discussed.