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

Hadronic phase in $\pi \pi$ and $K\bar{K}$ channels are calculated a la Regge. At the D mass one finds ${\delta }_{\pi \pi }\approx \pi \mathrm{/}3$ 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.