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Phases of elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix can beobtained using decays of $B$ mesons to $\pi^+ \pi^-$, $\pi^\pm K^\mp$, and$\pi^+ K^0$ or $\pi^- \overline{K}^0$. For $B^0~{\rm or}~ \overline{B}^0 \to\pi^+ \pi^-$, one identifies the flavor of the neutral $B$ meson at time ofproduction and studies the time-dependence of the decay rate. The otherprocesses are self-tagging and only their rates need be measured. By assumingflavor SU(3) symmetry and first-order SU(3) breaking, one can separatelydetermine the phases $\gamma \equiv {\rm Arg}~V_{ub}^*$ and $\alpha = \pi -\beta - \gamma$, where $\beta \equiv {\rm Arg}~V_{td}^*$. Special cases includethe vanishing of strong interaction phase differences between amplitudes, thepossibility of recovering partial information when $\pi^+ \pi^-$ and $\pi^\pmK^\mp$ decays cannot be distinguished from one another, and the use of acorrelation between $\gamma$ and $\alpha$ in the region of allowed parameters.Comment: 18 pages, 11 PostScript figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Weak phases from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>decays to kaons and charged pions

Weak phases fromBdecays to kaons and charged pions