Flavor-conservingCPphases in supersymmetry and implications for exclusiveBdecays

We study rare exclusive B decays based on the quark-level transition $\overrightarrow{b}{s\left(d\right)l}^{+}{l}^{-},$ where $l=e$ or $\mu ,$ in the context of supersymmetric theories with minimal flavor violation. We present analytic expressions for various mixing matrices in the presence of new $\mathrm{CP}$-violating phases, and examine their impact on observables involving B and $\overline{B}$ decays. An estimate is obtained for $\mathrm{CP}$-violating asymmetries in $\overline{B}\to K^{\left(*\right)}{l}^{+}{l}^{-}$ and $\overline{B}\to \rho (\pi {)l}^{+}{l}^{-}$ decays for the dilepton invariant mass region $1.2\hspace{0.5em}\mathrm{GeV}<M_{l^{+}{l}^{-}}<M_{J/\psi }.$ As a typical result, we find a $\mathrm{CP}$-violating partial width asymmetry of about $-6\%$ $(-5\%)$ in the case of $\overrightarrow{B}\pi$ $\left(\overrightarrow{B}\rho \right)$ in effective supersymmetry with phases of $\mathcal{O}\mathrm{}\left(1\right),$ taking into account the measurement of the inclusive $\overrightarrow{b}s\gamma$ branching fraction. On the other hand, $\mathrm{CP}$ asymmetries of less than 1% are predicted in the case of $\overrightarrow{B}{K}^{\left(*\right)}.$ We argue that it is not sufficient to have additional $\mathrm{CP}$ phases of $\mathcal{O}\mathrm{}\left(1\right)\mathrm{}$ to observe large $\mathrm{CP}$-violating effects in exclusive $\overrightarrow{b}{s\left(d\right)l}^{+}{l}^{-}$ decays.