Small violations of unitarity, the phase in Bs mixing and visible t->cZ decays at the LHC

We show that it is possible to accommodate the observed size of the phase in $B^0_s$--$bar B^0_s$, mixing in the framework of a model with violation of $3times 3$ unitarity. This violation is associated to the presence of a new $Q=2/3$ isosinglet quark $T$, which mixes both with $t$ and $c$ and has a mass not exceeding 500 GeV. The crucial point is the fact that this framework allows for $chiequivarg(-V_{ts}V_{cb}V_{tb}^*V_{cs}^*)$ of order $lambda$, to be contrasted with the situation in the Standard Model, where $chi$ is constrained to be of order $lambda^2$. We point out that this scenario implies rare top decays $tto cZ$ at a rate observable at the LHC and $|V_{tb}|$ significantly different from unity. In this framework, one may also account for the observed size of $D^0$--$bar D^0$ mixing without having to invoke long distance contributions. It is also shown that in the present scenario, the observed size of $D^0$--$bar D^0$ mixing constrains $chi^primeequivarg(-V_{cd}V_{us}V_{cs}^*V_{ud}^*)$ to be of order $lambda^4$, which is significantly smaller than what is allowed in generic models with violations of $3times 3$ unitarity.