Determining the weak phase gamma from charged B decays

A quadrangle relation is shown to be satisfied by the amplitudes for B+ --> pi(0)K(+), pi(+)K(0), eta K+, and eta'K+. By comparison with the corresponding relation satisfied by B- decay amplitudes, it is shown that the relative phases of all the amplitudes can be determined up to discrete ambiguities. Making use of an SU(3) relation between amplitudes contributing to the above decays and those contributing to B-+/- --> pi(+/-)pi(0), it is then shown that one can determine the weak phase gamma = Arg(V-ub*V-cb/V-us*V-cs), where V is the Cabibbo-Kobayashi-Maskawa matrix describing the charge-changing weak interactions between the quarks (u, c, t) and (d, s, b).