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 π⁺π⁻, π^±K⁺, and π⁺K⁰ or π⁻K̅⁰. For B⁰ or B̅⁰→π⁺π⁻, 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 to be measured. By assuming flavor SU(3) symmetry and first-order SU(3) breaking, one can separately determine the phases γ≡Arg V^∗_ub and α=π−β−γ, where β≡Arg V^∗_td. Special cases include the vanishing of strong interaction phase differences between amplitudes, the possibility of recovering partial information when π⁺π⁻ and π^±K^∓ decays cannot be distinguished from one another, and the use of a correlation between γ and α in the region of allowed parameters.