Renormalization Group Invariant Constraints among Coupling Constants in a Noncommutative Geometry Model

TL;DR

This paper investigates how coupling constants in a noncommutative geometry model of the standard model are constrained by renormalization group invariance, deriving new RGI constraints and exploring their relation to renormalizability.

Contribution

It introduces novel RGI constraints among coupling constants within the NCG framework and analyzes their implications for model renormalizability.

Findings

Derived two constraints on the Higgs mass evolution.

Identified RGI constraints in the NCG approach.

Explored the link between RGI constraints and multiplicative renormalizability.

Abstract

We study constraints among coupling constants of the standard model obtained in the noncommutative geometry (NCG) method. First, we analyze the evolution of the Higgs boson mass under the renormalization group by adopting the idea of \'Alvarez et al. For this analysis we derive two certain constraints by modifying Connes's way of constructing the standard model. Next, we find renormalization group invariant (RGI) constraints in the NCG method. We also consider the relation between the condition that a constraint among coupling constants of a model becomes RGI and the condition that the model becomes multiplicative renormalizable by using a simple example.