Can FCNC transition $c\to u{l}^{+}{l}^{-}$ be seen in $D\to V{l}^{+}{l}^{-}$ decays?

Abstract

The decays $D\to V{l}^{+}{l}^{-}$ present in principle the opportunity to observe the short distance FCNC transition $c\to u{l}^{+}{l}^{-}$, which is sensitive to the physics beyond the Standard Model. We analyze the $D\to V{l}^{+}{l}^{-}$ decays within the Standard Model, where in addition to the short distance dynamics also the long distance dynamics is present. The short distance contribution due to $c\to u{l}^{+}{l}^{-}$ transition, which is present only in the Cabibbo suppressed decays, is found to be three orders of magnitude smaller than the long distance contribution. The branching ratios well above $10^{-7}$ for Cabibbo suppressed decays could signal new physics. The most frequent decays are the Cabibbo allowed decays $D_s^{+}\to {\rho }^{+}{\mu }^{+}{\mu }^{-}$ and $D^0\to {\bar{K}}^{\ast 0}{\mu }^{+}{\mu }^{-}$, which are expected at the branching ratios of $3\cdot 10^{-5}$ and $1.7\cdot 10^{-6}$, respectively. These rates are not much lower than the present experimental upper limit.

Comments: 3 pages, latex, 3 figures, Talk given by S. Prelovsek at the Hyperons, Charm and Beauty Hadrons, Genova, Italy, 30 June -3 July 1998, to appear as proceedings in Nucl. Phys. B