SU(3) and CP violating weak and strong final state phases for B_{d}^{0} and B_{s}^{0} decays

Abstract

Using rotation in SU(3) space, a set of relations between various decay modes of B_{d} and B_{s} are derived. The decays bar{B}_{d}^{0}-> K^{*-}pi ^{+}(rho ^{+}K^{-}), bar{B}_{s}^{0}-> K^{*-}K^{+} are expressed in terms of decay parameters of bar{B}_{d}^{0}->rho ^{-}pi ^{+}(rho ^{+}\pi ^{-}). In particular the parameters r_{-+}(r_{+-}) of B_{d}->rho \pi decays are obtained in terms of experimentally known decay rates R_{-+}(R_{+-})=frac{1}{2}left(Gamma_{rho ^{+}pi ^{-}(rho ^{-}pi ^{+})}+\ar{\amma}_{\ho ^{-}pi ^{+}(rho ^{+}pi ^{-})}), $ R_{-+}^{prime}(R_{+-}^{prime})=frac{1}{2}left(Gamma_{K^{*+}pi ^{-}(rho ^{-}K^{+})}+bar{Gamma}_{K^{*-}\pi ^{+}(rho ^{+}K^{-})}), known parameters bar{lambda}, f_{K^{*}}/f_{rho}(f_{K}/f_{pi}) and two parameters B_{-+}=frac{R_{-+}}{left| T^{-+}right| ^{2}},B_{+-}=frac{R_{+-}}{| T^{+-}| ^{2}} which are determined by using factorization for tree amplitudes T^{-+} and T^{+-}. We find r_{-+}=0.21pm 0.04,r_{+-}=0.25pm 0.06. With these values the following bounds on left(z\equiv \cos \gamma \cos \delta, x=\sin \gamma sin \delta) are derived: [-0.34(-0.33)\leq z_{-+}(z_{+-})\leq 0.28(0.27) ] and [0.16(0.43)\leq x_{-+}(x_{+-})\leq 0.58(1.00) ] From (x,z) plot we obtain following bounds on weak phase gamma and strong phases \delta ^{prime}s z_{-+}>0,gamma geq 70^{circ},10^{circ} leq \delta _{-+}\leq 40^{circ}, z_{-+}<0,gamma geq 65^{\circ},$ $(180-\delta_{-+})$. For $\delta_{+-}$ we get $25^{\circ}leq \delta_{+-}\leq 90^{circ} or (180-delta_{+-}).