Decays D(s)+ → π(K)+l+l- and D0 → l+l- in the MSSM with and without R-parity

We study the rare decays D+ -> pi(+)l(+)l(-), D-s(+) -> K(+)l(+)l(-) and D-0 -> l(+)l(-) (l = e, mu) in the minimal supersymmetic standard model with and without R-parity. Using the strong constraints on relevant supersymmetric parameters from D-0 - (D) over bar (0) mixing and K+ -> pi(+)nu(nu) over bar decay, we examine constrained supersymmetry contributions to relevant branching ratios, direct CP violations and ratios of D-(s)(+) -> pi(K)(+)mu(+)mu(-) and D-(s)(+) -> 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)(+) -> pi(K)(+)l(+)l(-), moreover, the constrained LR and RL mass insertions still have obvious effects on the ratios of D-(s)(+) -> pi(K)(+)mu(+)mu(-) and D-(s)(+) -> pi(K)(+)e(+)e(-) decay rates. The direct CP asymmetries and the ratios of D-(s)(+) -> pi(K)(+)mu(+)mu(-) and D-(s)(+) -> 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)(+) -> pi(K)(+)l(+)l(-) are studied in detail.