Extraction of $V_{cb}$ from two-body hadronic B decays

We propose a method of extracting the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$ from two-body hadronic decay processes of $B\to DK$ with precisely determined form factors of $B$ meson semi-leptonic decays. The amplitude $M({\overline{B}}^0\to D^{+}{K}^{-})$ which does not include the effect of hadronic final state interactions can be theoretically evaluated by using factorization and form factors of semi-leptonic B decays. We can obtain all the amplitudes in an isospin relation $A(B^{-}\to D^0{K}^{-})=A({\overline{B}}^0\to D^{+}{K}^{-})+A({\overline{B}}^0\to D^0{\overline{K}}^0)$, including the effect of hadronic final state interactions as well as $V_{cb}$, using the experimental data of branching fractions of these three processes with a truncation of the states which contribute to the hadronic final state interactions. The extracted value of $V_{cb}$ is $(37\pm 6)\times {10}^{-3}$. The decay processes of $B\to D{K}^{\ast }$ and $B\to D^{\ast }K$ can also be used in the same way, and the extracted values of $V_{cb}$ are $(41\pm 7)\times {10}^{-3}$ and $(42\pm 9)\times {10}^{-3}$, respectively. This method becomes possible by virtue of recent precise determinations of the form factors of semi-leptonic B decays. The uncertainties of $V_{cb}$ by this method are expected to be reduced by the results of future B-factory experiments and lattice calculations.