Higgs boson mass and new physics

Abstract: We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alpha_s to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha_s (taken at 2sigma level) the bound reads M_H>=M_min (equality corresponds to the asymptotic safety prediction), where M_min=129+-6 GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of M_H with M_min would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scale a construction of an electron-positron or muon collider with a center of mass energy ~200+200 GeV (Higgs and t-quark factory) would be needed.

• The paper refines Higgs boson mass precision by employing three-loop renormalization group analysis and two-loop corrections to establish a lower bound near 129 ± 6 GeV.
• It demonstrates that a Higgs mass close to the computed lower limits supports the absence of new energy scales between the electroweak and Planck realms.
• The findings underscore the need for advanced experimental verification, recommending future colliders for dedicated Higgs and top-quark mass assessments.

Insights into the Paper: "Higgs Boson Mass and New Physics"

The paper "Higgs boson mass and new physics" features a crucial investigation into the Higgs boson mass within the framework of the Standard Model (SM) and examines its implications for new physics. The authors address two primary sources of lower bounds on the Higgs mass: the absolute stability of the SM vacuum and Higgs inflation. Additionally, they explore the prediction of the Higgs mass based on the asymptotic safety of the SM. This paper contributes an advancement over the conventional "one-loop matching–two-loop running" procedures by incorporating three-loop renormalization group (RG) analyses, along with selected two-loop corrections.

Numerical Precision and Predictions

One of the compelling results of this study is the reduction of the Higgs boson mass bounds' theoretical uncertainties—derived from SM physics—to 1 to 2 GeV. This improved precision is achieved through enhanced RG running procedures at the three-loop level. The authors find a Higgs mass lower bound of $M_{\text{min}} = 129 \pm 6$ GeV. This lower bound aligns well with the asymptotic safety scenario.

Implications for Beyond the SM Physics

The paper examines the implications of SM Higgs discovery within a particular mass range. Should the Higgs mass sit near the lower computed bounds, it would support the hypothesis that there are no new energy scales intervening between the electroweak scale and the Planck scale. Specifically, if the Higgs mass exactly equals $M_{\text{min}}$, it would hint at electroweak symmetry breaking being influenced by Planck-scale physics.

Experimental Relevance

The authors argue for the necessity of detailed experimental verification. They surmise that while the Large Hadron Collider (LHC) could potentially reduce some uncertainties, a more refined measurement of the Higgs and top-quark masses could necessitate a future electron-positron or muon collider to function as a dedicated Higgs and top-quark factory, with an operational energy of approximately 200 GeV.

Theoretical Significance

From a theoretical perspective, the paper explores various scenarios, such as the stability of the SM vacuum and the concept of metastability, where the Higgs mass is slightly above its minimum threshold, ensuring a universe lifetime exceeding the current epoch. The research additionally touches upon the implications of non-minimal coupling with gravity and the potential for Higgs-driven inflation, which further solidifies the importance of precisely knowing the Higgs mass.

Asymptotic Safety and the Higgs Mass

The concept of asymptotic safety, a possible non-perturbative UV completion for gravity, provides a unique insight into the Higgs mass predictions. The paper delineates how coupling constants in the SM, influenced by gravity's contribution to RG flow, might resolve into safe behavior at large scales. Such behavior necessitates the Higgs boson mass aligning closely with $M_{\text{min}}$.

Conclusion and Future Trajectories

In sum, this paper offers a rigorous and comprehensive study that narrows down the theoretical uncertainties surrounding the Higgs boson mass and examines the implications of various mass hypotheses. While the results make bold predictions regarding the absence of any intermediate energy scales, they hinge crucially on future experimental calibrations and verification. Continuous exploration at the intersection of SM and GR, especially in contexts like asymptotic safety or beyond the SM physics, remains a pivotal area for both theoretical and experimental efforts in high energy physics.