Measuring ${\hat{I}}^2$ in $B\to D^{\ast +}{D}^{\ast -}{K}_s$ Decays

Abstract

We consider the possibility of measuring both $\sin (2{\hat{I}}^2)$ and $\cos (2{\hat{I}}^2)$ in the KM unitarity triangle using the process $B^0\to D^{\ast +}{D}^{\ast -}{K}_s$. This decay mode has a higher branching fraction (O(1%)) than the mode $B^0\to D^{\ast +}{D}^{\ast -}$. We use the factorization assumption and heavy hadron chiral perturbation theory to estimate the branching fraction and polarization. The time dependent rate for $B^0(t)\to D^{\ast +}{D}^{\ast -}{K}_s$ can be used to measure $\sin (2{\hat{I}}^2)$ and $\cos (2{\hat{I}}^2)$ . Furthermore, examination of the $D^{\ast +}{K}_s$ mass spectrum may be the best way to experimentally find the broad $1^{+}$ p-wave $D_s$ meson.

Revtex, 28 pages, 7 figures, title changed, introduction expanded, added references, details of calculations moved to the appendix