Weak Phases From B Decays to Kaons and Charged Pions

Abstract

Phases of elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can be obtained using decays of $B$ mesons to ${\pi }^{+}{\pi }^{-}$, ${\pi }^{\pm }{K}^{\mp }$, and ${\pi }^{+}{K}^0$ or ${\pi }^{-}{\overline{K}}^0$. For $B^0\mathrm{or}{\overline{B}}^0\to {\pi }^{+}{\pi }^{-}$, one identifies the flavor of the neutral $B$ meson at time of production and studies the time-dependence of the decay rate. The other processes are self-tagging and only their rates need be measured. By assuming flavor SU(3) symmetry and first-order SU(3) breaking, one can separately determine the phases $\gamma \equiv \mathrm{Arg}{V}_{ub}^{\ast }$ and $\alpha =\pi -\beta -\gamma$, where $\beta \equiv \mathrm{Arg}{V}_{td}^{\ast }$. Special cases include the vanishing of strong interaction phase differences between amplitudes, the possibility of recovering partial information when ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{\pm }{K}^{\mp }$ decays cannot be distinguished from one another, and the use of a correlation between $\gamma$ and $\alpha$ in the region of allowed parameters.

Comments: 18 pages, 11 PostScript figures