Addendum to "Ultraviolet behaviour of Higgs inflation models"

TL;DR

This paper extends the analysis of scattering amplitudes in Higgs inflation models, clarifying the effective cutoff scales in different formulations and backgrounds, with implications for the models' ultraviolet behavior.

Contribution

It provides a detailed computation of on-shell scattering amplitudes in arbitrary inflaton backgrounds for Higgs inflation, comparing Einstein and Jordan frame cutoffs in Palatini and metric formulations.

Findings

Effective Einstein frame cutoff depends on the inflaton background in the $U(1)$ model.

In the realistic Higgs doublet model, the cutoff is $M_P/\sqrt{\xi}$ for both formulations.

The background inflaton field sets the effective Jordan frame cutoff in both formulations.

Abstract

This article is an addendum to [1]. We extend our computation of the on-shell scattering amplitudes in an arbitrary inflaton background $\bar{\phi}_1$. Although the effective Einstein frame cutoff for $\bar{\phi}_1>>M_P/\sqrt{\xi}$ turns out to be $\bar{\phi}_1$ or $\xi\bar{\phi}_1$ for the $U(1)$ model, this is not the case for the realistic doublet Higgs model where the effective Einstein frame cutoff turns out to be the standard $M_P/\sqrt{\xi}$ for both the Palatini and metric formulations. Then, as it has been pointed out in [1] the background $\bar{\phi}_1$ is the effective Jordan frame cutoff for both the Palatini and metric formulations.