Standard Model Higgs boson mass from inflation: two loop analysis

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}.

• The paper refines Higgs mass bounds by incorporating two-loop radiative corrections into the inflationary framework.
• The study employs two renormalization procedures, showing nearly invariant spectral index in one and mass-dependent variations in the other.
• The work benchmarks its results against previous studies and highlights the need for advanced computations to unify cosmology with particle physics.

Overview of "Standard Model Higgs boson mass from inflation: two loop analysis"

This paper extends previous analyses of the Standard Model Higgs inflation by incorporating two-loop radiative corrections into the effective potential. The main focus is on identifying how higher loop effects influence the bounds on the Higgs boson mass while maintaining the viability of the Standard Model (SM) as an effective field theory up to the Planck scale. Specifically, the Higgs mass bounds are slightly adjusted beyond the previously established range compatible with a robust SM framework, given the effects of two-loop corrections.

Key Insights and Numerical Results

• Higgs Mass Range: The paper provides an updated interval for the allowed Higgs mass $( m_\mathrm{min} < m_H < m_\mathrm{max}$) accounting for two-loop effects. This adjustment is crucial for Higgs field configurations that connect inflationary cosmology with particle physics without requiring new physics beyond the SM.
• Spectral Index Dependencies: The analysis elucidates the dependence of the spectral index $n_s$ of scalar perturbations on the Higgs mass. Two renormalization procedures are employed, grounded in different choice frames: the Einstein frame (procedure I) and the Jordan frame (procedure II). The former yields results for $n_s$ and the tensor-to-scalar ratio $r$ as $n_s = 0.97$ and $r = 0.0034$, largely invariant to the Higgs mass. In contrast, procedure II reveals a mass-dependent $n_s$ that deviates from the expected range for masses below $m_\mathrm{min}$.
• Comparison with Previous Work: The paper benchmarks its results against those from similar studies, particularly noting the contrasts with recent findings on radiative corrections and spectral indices.

Implications and Forward-Looking Perspectives

From a theoretical standpoint, the research underscores the sensitivity of inflationary potential predictions to higher-loop quantum corrections and the dependence on renormalization framing. These insights emphasize the necessity of precise theoretical frameworks and advanced computational approaches to accurately forecast cosmological parameters stemming directly from SM parameters.

Practically, this research highlights constraints that connect observable cosmological phenomena with particle physics parameters such as the Higgs mass. Such constraints become particularly relevant with upcoming observational data from cosmic microwave background (CMB) measurements and collider experiments aimed at the Higgs sector. By refining the understanding of Higgs-driven inflationary scenarios, this work might guide future experimental and theoretical initiatives geared toward unifying cosmology with particle physics.

In summary, this paper advances the methodology to connect Higgs physics with inflationary predictions and enhances the predictive power of the SM. As precision in theoretical calculations improves, further reconciliation between observation and theory will depend on addressing known gaps, such as inner loop corrections and potentially unknown physics at higher energy scales. This paper lays foundational insights for future developments in understanding the intersection of fundamental particle physics and cosmology.