Nonfactorizable contributions toB→D(*)Mdecays

Abstract

While the naive factorization assumption works well for many two-body nonleptonic B meson decay modes, the recent measurement of $\overline{B}\ensuremath{\rightarrow}{D}^{(*)0}{M}^{0}$ with $M=\ensuremath{\pi},$ $\ensuremath{\rho},$ and $\ensuremath{\omega}$ shows a large deviation from this assumption. We analyze the $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}M$ decays in the perturbative QCD approach based on the ${k}_{T}$ factorization theorem, in which both factorizable and nonfactorizable contributions can be calculated in the same framework. Our predictions for the Bauer-Stech-Wirbel parameters, $|{a}_{2}{/a}_{1}|=0.43\ifmmode\pm\else\textpm\fi{}0.04$ and $\mathrm{Arg}{(a}_{2}{/a}_{1})\ensuremath{\sim}\ensuremath{-}42\ifmmode^\circ\else\textdegree\fi{}$ and $|{a}_{2}{/a}_{1}|=0.47\ifmmode\pm\else\textpm\fi{}0.05$ and $\mathrm{Arg}{(a}_{2}{/a}_{1})\ensuremath{\sim}\ensuremath{-}41\ifmmode^\circ\else\textdegree\fi{},$ are consistent with the observed $\stackrel{\ensuremath{\rightarrow}}{B}D\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{*}\ensuremath{\pi}$ branching ratios, respectively. It is found that the large magnitude $|{a}_{2}|$ and the large relative phase between ${a}_{2}$ and ${a}_{1}$ come from color-suppressed nonfactorizable amplitudes. Our predictions for the ${B}^{0}\ensuremath{\rightarrow}{D}^{*0}{\ensuremath{\rho}}^{0}{,D}^{*0}\ensuremath{\omega}$ branching ratios can be confronted with future experimental data.