We show that simultaneous precision measurements of the $CP$-violating phase in time-dependent $B_s\to J/\psi \varphi$ study and the $B_s\to {\mu }^{+}{\mu }^{-}$ rate, together with measuring $m_{t^{\prime }}$ by direct search at the LHC, would determine $V_{t^{\prime }s}^{*}{V}_{t^{\prime }b}$ and therefore the $b\to s$ quadrangle in the four-generation standard model. The forward–backward asymmetry in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ provides further discrimination.

• Received 12 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.094027