Precision Constraints on Extra Fermion Generations

There has been recent renewed interest in the possibility of additional fermion generations. At the same time there have been significant changes in the relevant electroweak precision constraints, in particular, in the interpretation of several of the low energy experiments. We summarize the various motivations for extra families and analyze them in view of the latest electroweak precision data.

Figure 1

Individual $1\sigma$ constraints (39.35%) on $S$ and $T$. The contours assume $U=0$ and $M_H=117\mathrm{GeV}$ except for the central and upper 90% C.L. filled contours ($\Delta {\chi }^2=4.605$) allowed by all data. ${\alpha }_s$ is additionally constrained by the $\tau$ lifetime. Since the theory has changed, the strongly ${\alpha }_s$-dependent solid (dark green) contour from $Z$ line shape and cross section measurements [55] has moved significantly towards negative $S$ and $T$ compared to our previous analysis [22]. The long-dashed (magenta) contour from $\nu$ scattering has moved closer towards the global averages. The long-dash-dotted (indigo) contour from polarized $e$ scattering [56, 57] is near the upper tip of an elongated ellipse centered at $(S,T)=(-15,-21)$. The dash-dotted (black) contour from APV now agrees perfectly with the SM after the completion of a state-of-the-art atomic theory calculation [37]. The shaded (light green) $1\sigma$ ellipse shows the combined low energy data (APV and lepton scattering).

Figure 2

$S$ and $T$ for various mass splittings. The 90% C.L. ellipse is for $M_H=112\mathrm{GeV}$, while the solid line is the envelope for $M_H\ge 112\mathrm{GeV}$ with the kink arising from the Tevatron exclusion window, $131\mathrm{GeV}<M_H<204\mathrm{GeV}$ [58], in the presence of a fourth generation. Each symbol refers to a choice of $m_{t^{\prime }}^2-m_{b^{\prime }}^2$ (with $m_{b^{\prime }}=338\mathrm{GeV}$) which is increased in steps of $7,000{\mathrm{GeV}}^2$ starting with degeneracy (black circles). Likewise, moving from right to left increases $m_{l^{\prime }}^2-m_{{\nu }^{\prime }}^2$ (with $m_{{\nu }^{\prime }}=101\mathrm{GeV}$) by the same increments, where the third entries correspond to the choice of Ref. 33.