The Long Distance Contribution to $D\to\pi l^+l^-$

Abstract

We calculate the long distance contribution to $D^{+,0}\to\pi^{+,0}l^+l^-$ decays by the use of a vector meson dominance model, in which the $\phi$-meson plays the central role. The branching ratios obtained are $10^{-6}$ and a few times $10^{-7}$ for the resonance and non-resonance regions respectively. The analysis includes a calculation of $D^+\to\pi^+\phi$, consistent with the experimental value.