Hadronic Phases and Isospin Amplitudes in $D(B) \to \pi \pi$ and $D(B) \to K \bar K$ Decays

Abstract

Hadronic phase in $\pi \pi$ and $K \bar K$ channels are calculated a la Regge. At the D mass one finds $\delta_{\pi \pi} \approx \pi/3$ and $\delta_{K \bar K} \approx -\pi/6$ in good agreement with the CLEO data while at the B mass these angles are predicted to be, respectively, $11^\circ$ and $-7^\circ$. With the hadronic phase $e^{i \delta_{K \bar K}}$ taken into account, a quark diagram decomposition of the isospin invariant amplitudes in $D \to K \bar K$ decays fits the data provided the exchange diagram contribution is about 1/3 of the tree level one.