The top quark and Higgs boson masses and the stability of the electroweak vacuum (1207.0980v3)

Abstract: The ATLAS and CMS experiments observed a particle at the LHC with a mass $\approx 126$ GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to high scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be $M_H \gsim 129 \pm 1$ GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, $m_t^{\rm exp}=173.2 \pm 0.9$ GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive $p \bar p \to t\bar t +X$ cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the $\bar{\rm MS}$-scheme to be $m_t^{\bar{\rm MS}}(m_t) = 163.3 \pm 2.7$ GeV which gives a top quark pole mass of $m_t^{\rm pole}= 173.3 \pm 2.8$ GeV. This leads to the vacuum stability constraint $M_H \geq 129.8 \pm 5.6$ GeV to which a $\approx 126$ GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron-positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy.

• The paper investigates the impact of Higgs (~126 GeV) and top quark masses on the stability of the electroweak vacuum.
• It proposes using top quark pair production cross-sections to derive a more accurate top quark mass measurement.
• The study emphasizes that future precision experiments are crucial to validate the Standard Model and assess vacuum stability.

The Top Quark and Higgs Boson Masses and the Stability of the Electroweak Vacuum

The paper under review examines a fundamental question in the domain of particle physics and cosmology: can the Standard Model (SM) be consistently extrapolated up to very high-energy scales while maintaining stability in the electroweak vacuum? Specifically, it investigates the interplay between the masses of the Higgs boson and the top quark in determining this stability.

Summary of Key Findings

1. Higgs Boson Mass Observations: The ATLAS and CMS collaborations have observed a Higgs-like particle with a mass of approximately 126 GeV. This finding aligns with expectations for the SM Higgs boson and raises questions about vacuum stability when the SM is extended to higher energy scales.
2. Vacuum Stability Condition: The stability of the electroweak vacuum hinges upon the Higgs boson mass, which ideally should be above approximately 129 GeV to maintain stability up to the Planck scale. However, this requirement is contingent on the top quark's mass input, traditionally measured at the Tevatron as 173.2 ± 0.9 GeV.
3. Top Quark Mass Determination: The authors argue for using the total cross-section of top quark pair production at hadron colliders as a more precise method for determining the top quark mass. They derive a running mass in the $\overline{\text{MS}}$ scheme as 163.3 ± 2.7 GeV, leading to a top quark pole mass of 173.3 ± 2.8 GeV.
4. Implications for Electroweak Vacuum Stability: Given the derived top quark mass, the stability of the electroweak vacuum requires a Higgs mass of M_H ≥ 129.8 ± 5.6 GeV. The current estimates of the Higgs mass being about 126 GeV are consistent with maintaining vacuum stability, given the uncertainties.
5. Future Prospects for Precision Measurements: The authors emphasize that more precise determinations of the top quark pole mass can be achieved with a high-energy electron-positron collider, potentially reaching accuracies of 200 MeV. Such precision will be critical in affirming the stability of the electroweak vacuum.

Implications and Future Developments

This research has profound implications for the long-term viability of the Standard Model and the possible scenarios extending beyond it. The interplay between the Higgs and top quark masses is crucial for understanding the fate of our universe at remote energy scales—possibly revealing insights into novel physics outside the reach of current particle accelerators.

Moreover, the development of future collider experiments, particularly those focusing on electron-positron collisions, will be vital for verifying predictions concerning vacuum stability. Precision measurements gained from these experiments could either strengthen the robustness of the SM or expose new deviations hinting at physics beyond the SM.

Conclusion

In conclusion, the authors provide an exhaustive analysis of the interplay between the Higgs boson and top quark masses in influencing electroweak vacuum stability. The findings underscore the critical role of precision measurements in advancing our understanding of particle physics, potentially steering future research directions toward deeper theoretical insights or advanced experimental methodologies. Additionally, this analysis paves the way for extensive investigations that could explore the boundaries and possible extensions of the established SM framework.