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Addendum to "Ultraviolet behaviour of Higgs inflation models"

This article is an addendum to [1]. We extend our computation of the on-shell scattering amplitudes in an arbitrary inflaton background $\barϕ_1$. Although the effective Einstein frame cutoff for $\barϕ_1>>M_P/\sqrtξ$ turns out to be $\barϕ_1$ or $ξ\barϕ_1$ 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 $M_P/\sqrtξ$ for both the Palatini and metric formulations. Then, as it has been pointed out in [1] the background $\barϕ_1$ is the effective Jordan frame cutoff for both the Palatini and metric formulations.