Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model

TL;DR

This paper uses the functional renormalization group to derive bounds on the Higgs mass within a simplified Yukawa model, revealing how bare potential choices influence these bounds and their implications for the standard model.

Contribution

It demonstrates how the renormalization group flow determines Higgs mass bounds and shows that more general bare potentials can lower these bounds significantly.

Findings

Finite Higgs mass bounds emerge from the RG flow.

More general bare potentials can reduce the lower Higgs mass bound.

Small Higgs masses may not imply new physics or instability.

Abstract

We study the functional renormalization group flow of a Higgs-Yukawa toy model mimicking the top-Higgs sector of the standard model. This approach allows for treating arbitrary bare couplings. For the class of standard bare potentials of \phi^4-type at a given ultraviolet cut-off, we show that a finite infrared Higgs mass range emerges naturally from the renormalization group flow itself. Higgs masses outside the resulting bounds cannot be connected to any conceivable set of bare parameters in this standard-model \phi^4 class. By contrast, more general bare potentials allow to diminish the lower bound considerably. We identify a simple renormalization group mechanism for this depletion of the lower bound. If active also in the full standard model, Higgs masses smaller than the conventional infrared window do not necessarily require new physics at low scales or give rise to instability problems.