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.

Comments: 10pages,latex