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 ^{-})}), $R_{-+}^{prime}(R_{+-}^{prime})=frac12left(Gamm{a}_{K^{\ast +}p{i}^{-}(rh{o}^{-}{K}^{+})}+bar{Gamma}_{K^{\ast -}{\pi }^{+}(rh{o}^{+}{K}^{-})}),knownparametersbarlambda,f_{K^{\ast }}/f_{rho}(f_K/f_{pi})andtwoparameters{B}_{-+}=frac{R}_{-+}left|T^{-+}right{|}^2,B_{+-}=frac{R}_{+-}|T^{+-}{|}^{2}whicharedeterminedbyusingfactorizationfortreeamplitudes{T}^{-+}and{T}^{+-}.Wefind{r}_{-+}=0.21pm0.04,r_{+-}=0.25pm\mathrm{0.06.}Withthesevaluesthefollowingboundsonleft(z\equiv \cos \gamma \cos \delta ,x=\sin \gamma sin\delta )arederived:[-0.34(-0.33)\le z_{-+}(z_{+-})\le 0.28(0.27)]and[0.16(0.43)\le x_{-+}(x_{+-})\le 0.58(1.00)]From(x,z)plotweobtainfollowingboundsonweakphasegammaandstrongphases{\delta }^{prime}s{z}_{-+}>0,gammageq70^{circ},10^{circ}leq{\delta }_{-+}\le 40^{circ},z_{-+}<0,gammageq65^{\circ },$ $(180-{\delta }_{-+})$. For ${\delta }_{+-}$ we get $25^{\circ}leq \delta_{+-}\leq 90^{circ} or (180-delta_{+-}).

Comments: 17 pages, 2 figures; Abstract and results are modified