Constraining the mixing matrix for Standard Model with four generations: time dependent and semi-leptonic CP asymmetries in $B_d^0$, $B_s$ and $D^0$

Abstract

Using existing experimental information from K, B and D decays as well as electroweak precision tests and oblique parameters, we provide constraints and correlations on the parameters of the 4X4 mixing matrix for the Standard Model with four generations (SM4). We emphasize that some correlations amongst the parameters have important repercussions for key observables. We work with a particular representation of this matrix which is highly suited for extracting information from B-decays. Implications of the resulting constraints for time dependent and semileptonic CP asymmetries for $D^0$, $B^0$ and for $B_s$ are also given. While we show that the semi-leptonic asymmetries may be significantly enhanced in SM4 over the SM, there are important constraints and correlations with other observables. In this context we suggest that existing data from B-factories taken on $\Upsilon (4S)$ and $\Upsilon (5S)$, and in the relevant continuum be used to constrain the semi-leptonic asymmetries for $B_d$, $B_s$ as well as their linear combination. Of course, the data from the Tevatron and LHCb experiments can provide non-trivial tests of SM4 as well.