Decays $D_{(s)}^{+}\to \pi (K{)}^{+}{\ell }^{+}{\ell }^{-}$ and $D^0\to {\ell }^{+}{\ell }^{-}$ in the MSSM with and without R-parity

Abstract

We study the rare decays $D^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$, $D_s^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ and $D^0\to {\ell }^{+}{\ell }^{-}(\ell =e,\mu )$ in the minimal supersymmetic standard model with and without R-parity. Using the strong constraints on relevant supersymmetric parameters from $D^0-{\bar{D}}^0$ mixing and $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ decay, we examine constrained supersymmetry contributions to relevant branching ratios, direct CP violations and ratios of $D_{(s)}^{+}\to \pi (K{)}^{+}{\mu }^{+}{\mu }^{-}$ and $D_{(s)}^{+}\to \pi (K{)}^{+}{e}^{+}{e}^{-}$ decay rates. We find that both R-parity conserving LR as well as RL mass insertions and R-parity violating squark exchange couplings have huge effects on the direct CP violations of $D_{(s)}^{+}\to \pi (K{)}^{+}{\ell }^{+}{\ell }^{-}$, moreover, the constrained LR and RL mass insertions still have obvious effects on the ratios of $D_{(s)}^{+}\to \pi (K{)}^{+}{\mu }^{+}{\mu }^{-}$ and $D_{(s)}^{+}\to \pi (K{)}^{+}{e}^{+}{e}^{-}$ decay rates. The direct CP asymmetries and the ratios of $D_{(s)}^{+}\to \pi (K{)}^{+}{\mu }^{+}{\mu }^{-}$ and $D_{(s)}^{+}\to \pi (K{)}^{+}{e}^{+}{e}^{-}$ decay rates are very sensitive to both moduli and phases of relevant supersymmetric parameters. In addition, the differential direct CP asymmetries of $D_{(s)}^{+}\to \pi (K{)}^{+}{\ell }^{+}{\ell }^{-}$ are studied in detail.

Comments: 18 pages, 9 figures