Rare charm meson decaysD→Pl+l−andc→ul+l−in the standard model and the minimal supersymmetric standard model

Abstract

We study the nine possible rare charm meson decays $\stackrel{\ensuremath{\rightarrow}}{D}{\mathrm{Pl}}^{+}{l}^{\ensuremath{-}}$ $(P=\ensuremath{\pi},K,\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}})$ using heavy meson chiral Lagrangians and find them to be dominated by the long distance contributions. The decay ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{l}^{+}{l}^{\ensuremath{-}},$ with a branching ratio $\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6},$ is expected to have the best chances for an early experimental discovery. The short distance contribution in the five Cabibbo suppressed channels arises via the $\stackrel{\ensuremath{\rightarrow}}{c}{\mathrm{ul}}^{+}{l}^{\ensuremath{-}}$ transition; we find that this contribution is detectable only in the $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\pi}{l}^{+}{l}^{\ensuremath{-}}$ decay, where it dominates the differential spectrum at high-${q}^{2}.$ The general minimal supersymmetric standard model can enhance the $\stackrel{\ensuremath{\rightarrow}}{c}{\mathrm{ul}}^{+}{l}^{\ensuremath{-}}$ rate by up to an order of magnitude; its effect on the $\stackrel{\ensuremath{\rightarrow}}{D}{\mathrm{Pl}}^{+}{l}^{\ensuremath{-}}$ rates is small since the $\stackrel{\ensuremath{\rightarrow}}{c}{\mathrm{ul}}^{+}{l}^{\ensuremath{-}}$ enhancement is sizable in the low-${q}^{2}$ region, which is inhibited in the hadronic decay.