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

Research paper by ** Fayyazuddin**

Indexed on: **15 Feb '07**Published on: **15 Feb '07**Published in: **High Energy Physics - Phenomenology**

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join for free

#### 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_{+-}).