Nonleptonic Cabibbo Favoured $B$-Decays and $CP$-Asymmetries for Charmed Final Hadron States in Isgur and Wise Theory

Abstract

The Cabibbo allowed non-leptonic $B$-decays in two hadrons are studied, within the factorization hypothesis, in the framework of Isgur and Wise theory for the matrix elements of the $ΔB=-ΔC=\pm 1$ weak currents. The $SU(2)_{HF}$ symmetry relates $|ΔB|=1$ to $|ΔC|=1$ currents, which have been measured in the semileptonic strange decays of charmed particles. By assuming colour screening and allowing for $SU(3)$ invariant contributions from the annihilation terms with charmed final states one is able to comply with the present experimental knowledge.\\ The $CP$ violating asymmetries in neutral $B$ decays are given for charmed final states in terms of the $K-M$ angles. With the central values found for the annihilation parameters there is a destructive (constructive) interference between the direct and annihilation terms in the Cabibbo allowed (doubly forbidden) amplitudes for the decays into $D^{0}(D^{*0})π^0$ and $D^0ρ^0$ so that they may be of the same order. This would imply large asymmetries, for which however our present knowledge on the amplitudes does not allow to predict even their sign.\\ We have better confidence in our predictions for the charged final states than the neutral ones and can draw the conclusion that the detection of the corresponding asymmetries requires, at least, $10^6$ tagged neutral $B$-particles.