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 $B_s^0$–${\bar{B}}_s^0$, mixing in the framework of a model with violation of $3\times 3$ unitarity. This violation is associated to the presence of a new $Q=2\mathrm{/}3$ 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 $\chi \equiv \arg (-V_{ts}{V}_{cb}{V}_{tb}^{\ast }{V}_{cs}^{\ast })$ 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 $t\to cZ$ at a rate observable at the LHC and $\mathrm{\mid }{V}_{tb}\mathrm{\mid }$ 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 ${\chi }^{\mathrm{\prime }}\equiv \arg (-V_{cd}{V}_{us}{V}_{cs}^{\ast }{V}_{ud}^{\ast })$ to be of order ${\lambda }^4$, which is significantly smaller than what is allowed in generic models with violations of $3\times 3$ unitarity.