Standard Model Higgs boson mass from inflation: two loop analysis

TL;DR

This paper refines the Standard Model Higgs inflation analysis by including two-loop corrections, examining how these affect the Higgs mass range and the predictions for scalar perturbations in different renormalization schemes.

Contribution

It provides a two-loop level analysis of Higgs inflation, revealing how higher-order effects modify the allowed Higgs mass interval and the inflationary predictions in different frames.

Findings

Higher loop effects slightly extend the allowed Higgs mass range.

In the Einstein frame, spectral index and tensor-to-scalar ratio are nearly independent of Higgs mass.

In the Jordan frame, the spectral index depends on the Higgs mass and can fall outside the viable range.

Abstract

We extend the analysis of \cite{Bezrukov:2008ej} of the Standard Model Higgs inflation accounting for two-loop radiative corrections to the effective potential. As was expected, higher loop effects result in some modification of the interval for allowed Higgs masses m_min<m_H<m_max, which somewhat exceeds the region in which the Standard Model can be considered as a viable effective field theory all the way up to the Planck scale. The dependence of the index n_s of scalar perturbations on the Higgs mass is computed in two different renormalization procedures, associated with the Einstein (I) and Jordan (II) frames. In the procedure I the predictions of the spectral index of scalar fluctuations and of the tensor-to-scalar ratio practically do not depend on the Higgs mass within the admitted region and are equal to n_s=0.97 and r=0.0034 respectively. In the procedure II the index n_s acquires the visible dependence on the Higgs mass and and goes out of the admitted interval at m_H below m_min. We compare our findings with the results of \cite{DeSimone:2008ei}.