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

Abstract

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 $\mathcal{M}(\bar{B}^0 \to D^+ K^-)$ 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 $\mathcal{A}(B^-\to D^0K^-) =\mathcal{A}(\bar{B}^0\to D^+K^{-})+\mathcal{A}(\bar{B}^0\to D^{0}\bar{K}^0)$ 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 $B\to DK^{*}$ and $B\to D^{*}K$ 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.