Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision

Abstract: We perform a manifestly gauge-independent analysis of the vacuum stability in the Standard Model (SM) including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the $\overline{\mathrm{MS}}$ Higgs self-coupling and its beta function and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the SM be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with Monte Carlo mass quoted by the Particle Data Group at the $1.3\sigma$ level.

• The paper presents an advanced gauge-independent analysis of electroweak vacuum stability using two-loop matching, three-loop RG evolution, and four-loop QCD corrections.
• It establishes a refined upper bound on the top quark pole mass, providing insights into whether the electroweak vacuum is stable or metastable up to the Planck scale.
• The study underscores significant cosmological implications and invites more precise experimental measurements to explore potential physics beyond the Standard Model.

Stability of the Electroweak Vacuum: Gauge Independence and Precision Analysis

This paper presents a comprehensive study on the stability of the electroweak vacuum in the standard model (SM) that is both gauge-independent and grounded with advanced precision. Key elements of this research include two-loop matching, three-loop renormalization group (RG) evolution, and pure QCD corrections up to four loops. The authors disregard light-fermion masses for simplification while focusing on heavy-fermion contributions.

The motivating factor behind this study is the quest to determine vacuum stability up to the Planck scale, which yields insights into the universe's fate and the necessity (or lack thereof) for theories extending beyond the SM. The determination relies on the nullification of the Higgs self-coupling and its beta function in a sophisticated renormalization scheme. Given the Higgs boson's discovery with a mass around 125.7 GeV, confirming its properties predicted by the SM, this analysis takes on a substantiated precision to affirm or rule out potential new physics.

The analysis yields an upper bound on the pole mass of the top quark, identified as $M_t^\mathrm{cri}$, which is compatible with the Monte Carlo mass determined by the Particle Data Group at about the 1.3σ level. Specifically, the work finds $$M_t^\mathrm{cri} = 171.44 \pm 0.30{+0.17\atop-0.36}$$ GeV, incorporating experimental and theoretical uncertainties. This raises important discussions about whether the vacuum is truly metastable, a notion frequently assumed given current experimental constraints but possibly premature without accounting for unknown relationships between experimental top-quark mass determinations and theoretical calculations.

The results are not just of theoretical interest. Understanding vacuum stability has profound cosmological implications, as it relates to Higgs potential's second minimum and whether our electroweak vacuum could transition to a deeper state, potentially destabilizing current physical laws. This study significantly enhances theoretical rigor by using gauge-independent methods and by employing advanced calculations, bringing us closer to understanding whether the SM requires extensions to address outstanding physics questions like neutrino masses, dark matter, and the baryon asymmetry in the universe.

The implications of this work are manifold. The refined analysis serves not only as a litmus test for future avowals or refutations surrounding universality and completeness in the SM but also as an impetus for more precise experimental measurements of SM parameters. It raises the prospects of further exploring how closely the current universe's parameters are tuned to vacuum stability, and whether such fine-tuning suggests underlying principles or physics beyond the SM.

In the broader context of AI and simulation, the meticulous detail and multi-loop calculations employed here exemplify the precision and care necessary for complex systems analysis, which can extend to the computational simulations and algorithms optimally used in artificial intelligence research. Understanding and managing such intricacy could have ripple effects across computational sciences, encouraging advancements in methods handling large datasets with precision. As the dialogue between theoretical prediction and experimental verification continues to mature, so too will our understanding of the fundamental physics governing our universe.