Determining the Weak Phase $γ$ From Charged $B$ Decays

Details Determining the Weak Phase $γ$ From Charged $B$ Decays Determining the Weak Phase $γ$ From Charged $B$ Decays

1995-09-18

arxiv.org/abs/hep-ph/9509325v1

Phys.Rev. D53 (1996) 2516-2522

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, latex, 7 uuencoded figures

Scientific paper

10.1103/PhysRevD.53.2516

A quadrangle relation is shown to be satisfied by the amplitudes for $B^+ \to \pi^0 K^+,~\pi^+ K^0,~\eta K^+$, 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 $B^{\pm} \to \pi^{\pm} \pi^0$, it is then shown that one can determine the weak phase $\gamma \equiv {\rm Arg} (V_{ub}^* V_{cb}/V_{us}^* V_{cs})$, where $V$ is the Cabibbo-Kobayashi-Maskawa matrix describing the charge-changing weak interactions between the quarks $(u,c,t)$ and $(d,s,b)$.

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