Impact of a Higgs Boson at a Mass of 126 GeV on the Standard Model with Three and Four Fermion Generations

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 measured at LEP and SLD, and the latest determinations of $M_W$, $m_t$, and ${\alpha }_s$. For the three-generation case we analyze 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 electroweak precision observables from their best-fit values. Our indirect prediction of the top mass is $m_t={175.7}_{-2.2}^{+3.0}\mathrm{GeV}$ at 68.3% C.L., which is in good agreement with the direct measurement. We also plot the preferred area in the $M_W\mathrm{\text{−}}{m}_t$ plane. The best-fit Higgs boson 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 $H\to \gamma \gamma$ 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 $H\to b\overline{b}$ the significance drops to $4.8\sigma$.

Figure 1

Deviations of the EWPOs in the standard model. The observables were calculated with ZFitter [42, 43, 44]. For an observable $\mathcal{O}$ with experimental value ${\mathcal{O}}_{\exp }$, experimental error $\Delta {\mathcal{O}}_{\exp }$, and best-fit prediction ${\mathcal{O}}_{\mathrm{fit}}$, we define the deviation as $({\mathcal{O}}_{\exp }-{\mathcal{O}}_{\mathrm{fit}})/\Delta {\mathcal{O}}_{\exp }$.

Figure 2

The 68.3%, 95.5%, and 99.7% C.L. regions in the $m_t\mathrm{\text{−}}{M}_W$ plane using Higgs signal strengths and EWPOs. Also shown are the experimental values of $m_t$ and $M_W$ and their errors. The inner error bars are the statistical errors.

Figure 3

Deviations (defined as in Fig. 1) of the Higgs signal strengths for the SM (blue) and for the SM4 (red) at a fixed Higgs mass of 126 GeV. For comparison, the results of the fit to pre-ICHEP2012 data from Ref. 18 are also shown in green. In the right column we show, for the SM4 fit to current data, the change in the minimum ${\chi }^2$ value when the corresponding signal strength is removed from the fit.

Figure 4

Higgs mass scan for the SM (blue line) and the SM4 (red line) based on the input set in the second column of Table .