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 measured at LEP and SLD, and the latest determinations of ${M}_{W}$, ${m}_{t}$, and ${\ensuremath{\alpha}}_{s}$. 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 ${m}_{t}={175.7}_{\ensuremath{-}2.2}^{+3.0}\text{ }\text{ }\mathrm{GeV}$ at 68.3% C.L., which is in good agreement with the direct measurement. We also plot the preferred area in the ${M}_{W}\mathrm{\text{\ensuremath{-}}}{m}_{t}$ 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 $H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ signal strength now disagrees with its best-fit SM4 value at more than $4\ensuremath{\sigma}$. We perform a likelihood-ratio test to compare the SM and SM4 and show that the SM4 is excluded at $5.3\ensuremath{\sigma}$. Without the Tevatron data on $H\ensuremath{\rightarrow}b\overline{b}$ the significance drops to $4.8\ensuremath{\sigma}$.