$V_{td}$ from Hadronic Two-Body $B$ Decays

Abstract

Certain hadronic two-body decays of $B$ mesons are dominated by penguin diagrams. The ratios of rates for several such decays, including $Γ(B^0 \to \overline{K}^{*0} K^0)/Γ(B^0 \to ϕK^0)$, $Γ(B^0 \to \overline{K}^{*0} K^{*0})/Γ(B^0 \to ϕK^{*0})$, $Γ(B^+ \to \overline{K}^{*0} K^+)$ $/Γ(B^+ \to ϕK^+)$, and $Γ(B^+ \to \overline{K}^{*0} K^{*+})/Γ(B^+ \to ϕK^{*+})$, 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.