V$_{td}$ from hadronic two-body B decays

Certain hadronic two-body decays of B mesons are dominated by penguin diagrams. The ratios of rates for several such decays, including \Gamma(B^0 \to \overline{K}^{*0} K^0)/\Gamma(B^0 \to \phi K^0), \Gamma(B^0 \to \overline{K}^{*0} K^{*0})/\Gamma(B^0 \to \phi K^{*0}), \Gamma(B^+ \to \overline{K}^{*0} K^+) /\Gamma(B^+ \to \phi K^+), and \Gamma(B^+ \to \overline{K}^{*0} K^{*+})/\Gamma(B^+ \to \phi K^{*+}), can provide information on the ratio of Cabibbo-Kobayashi-Maskawa (CKM) elements |V_{td}/V_{ts}| in a manner complementary to other proposed determinations. SU(3) breaking effects cancel in some ratios. The cases of neutral B decays are free of corrections from small annihilation terms.