Less space for a new family of fermions

We investigate the experimentally allowed parameter space of an extension of the standard model (SM3) by one additional family of fermions. Therefore we extend our previous study of the CKM like mixing constraints of a fourth generation of quarks. In addition to the bounds from tree-level determinations of the 3$\times$3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s γ$) we also investigate the electroweak $S$, $T$, $U$ parameters, the angle $γ$ of the unitarity triangle and the rare decay $B_s \to μ^+ μ^-$. Moreover we improve our treatment of the QCD corrections compared to our previous analysis. We also take leptonic contributions into account, but we neglect the mixing among leptons. As a result we find that typically small mixing with the fourth family is favored, but still some sizeable deviations from the SM3 results are not yet excluded. The minimal possible value of $V_{tb}$ is 0.93. Also very large CP-violating effects in $B_s$ mixing seem to be impossible within an extension of the SM3 that consists of an additional fermion family alone. We find a delicate interplay of electroweak and flavor observables, which strongly suggests that a separate treatment of the two sectors is not feasible. In particular we show that the inclusion of the full CKM dependence of the $S$ and $T$ parameters in principle allows the existence of a degenerate fourth generation of quarks.

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