Impact of a Higgs boson at a mass of 126 GeV on the standard model with three and four fermion generations

Abstract: We perform a comprehensive statistical analysis of the standard model (SM) with three and four generations using the latest Higgs search results from LHC and Tevatron, the electroweak precision observables (EWPOs) measured at LEP and SLD and the latest determinations of M_W, m_t and alpha_s. For the three-generation case we analyse the tensions in the electroweak fit by removing individual observables from the fit and comparing their predicted values with the measured ones. In particular, we discuss the impact of the Higgs search results on the deviations of the EWPOs from their best-fit values. Our indirect prediction of the top mass is m_t=175.7(+3.0)(-2.2) GeV at 68.3% CL, in good agreement with the direct measurement. We also plot the preferred area in the M_W - m_t plane. The best-fit Higgs mass is 126.0 GeV. For the case of the SM with a perturbative sequential fourth fermion generation (SM4) we discuss the deviations of the Higgs signal strengths from their best-fit values. The H -> gamma gamma signal strength now disagrees with its best-fit SM4 value at more than 4 sigma. We perform a likelihood-ratio test to compare the SM and SM4 and show that the SM4 is excluded at 5.3 sigma. Without the Tevatron data on H -> b bbar the significance drops to 4.8 sigma.

Analysis of the Impact of a 126 GeV Higgs Boson on Different Fermion Generations within the Standard Model

The paper by Eberhardt et al. delves into the implications of the Higgs boson with a mass of 126 GeV on the Standard Model (SM), considering scenarios involving three and four fermion generations. The research integrates data from the Large Hadron Collider (LHC) and Tevatron with Electroweak Precision Observables (EWPOs) from LEP and SLD, alongside the latest measurements of the W boson mass ($M_W$), the top quark mass ($m_t$), and the strong coupling constant ($\alpha_s$).

Key Findings

In the three-generation SM context, the paper scrutinizes tensions observed within the electroweak fit, isolating individual observables to identify deviations from their optimal values. Notably, the paper highlights an indirect prediction for the top quark mass: (m_t = 175.7^{+3.0}_{-2.2}) GeV at a 68.3% confidence level, aligning well with direct empirical measurements. Moreover, the preferred Higgs mass emerges at 126.0 GeV, consistent with the LHC's findings.

A striking aspect of the analysis is the treatment of an additional fermion generation (SM4). The presence of a sequential fourth generation generates significant deviations in Higgs signal strengths, particularly for the $H\to\gamma\gamma$ decay mode, which diverges by over 4 sigma. The SM4 hypothesis is evaluated through a likelihood-ratio test, yielding exclusion at a 5.3 sigma confidence level, although this significance diminishes slightly when Tevatron data on $H\to b \bar b$ is omitted.

Implications and Future Directions

This paper contributes to a nuanced understanding of the SM's consistency with Higgs data, reinforcing the three-generation framework's robustness with only minor tensions in specific electroweak sectors. Notably, it establishes a decisive statistical argument against the SM4 within the confinements of a minimal Higgs sector.

Practically, these results limit the parameter space for theorists proposing more complex models beyond the known three generations. While the non-decoupling effects of heavy fermions in the SM4 scenario generate detectable deviations, they also accentuate the challenges of accurately quantifying statistical significances without nested model frameworks.

Theoretically, these insights invite rigorous exploration of alternative new physics, particularly models capable of reconciling existing data with minimal extraneous assumptions. Future work might further probe the parameter spaces of models with expanded Higgs sectors or non-perturbative behaviors, which could potentially evade current experimental constraints.

Eberhardt et al. offer a comprehensive evaluation of the SM through rigorous statistical methods, advancing the discourse on potential fourth-generation effects in light of contemporary Higgs data and setting a benchmark for subsequent analyses as experimental precision continues to enhance.