We show that it is possible to accommodate the observed size of the phase in $B_s^0-{\overline{B}}_s^0$ mixing in the framework of a model with violation of $3\times 3$ unitarity. This violation is associated to the presence of a new $Q=2/3$ 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 $\chi \equiv \arg (-V_{ts}{V}_{cb}{V}_{tb}^{*}{V}_{cs}^{*})$ 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 $t\to cZ$ 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 $D^0-{\overline{D}}^0$ mixing without having to invoke long-distance contributions. It is also shown that in the present scenario, the observed size of $D^0-{\overline{D}}^0$ mixing constrains ${\chi }^{\prime }\equiv \arg (-V_{cd}{V}_{us}{V}_{cs}^{*}{V}_{ud}^{*})$ to be of order ${\lambda }^4$, which is significantly smaller than what is allowed in generic models with violations of $3\times 3$ unitarity.

• Received 7 January 2009

DOI:https://doi.org/10.1103/PhysRevD.79.096009