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We study the rare decays $B^{+}_u\to \pi^{+}\ell^{+}\ell^{-}$,$\rho^{+}\ell^{+}\ell^{-}$ and $B^{0}_d \to \ell^{+} \ell^{-}(\ell=e,\mu)$ inthe R-parity violating supersymmetric standard model. From the latest upperlimits of $\mathcal{B}(B^+_u\to\pi^+\ell^+\ell^-)$ and$\mathcal{B}(B^0_d\to\ell^+\ell^-)$, we have derived new upper bounds on therelevant R-parity violating couplings products, which are stronger than theexisting ones. Using the constrained parameter space, we present the R-parityviolating effects on the branching ratios and the forward-backward asymmetriesof these decays. We find that $\mathcal{B}(B^0_d\to \ell^+\ell^-)$ and$\mathcal{B}(B^+_u \to\rho^+\ell^+\ell^-)$ could be enhanced several orders bythe R-parity violating sneutrino and squark exchanges, respectively. TheR-parity violating effects on the dilepton invariant mass spectra of $B^+_u\to\pi^+\ell^+\ell^-$, $\rho^+\ell^+\ell^-$ and the normalized forward-backwardasymmetry $\mathcal{A}_{FB}(B^+_u\to\pi^+\ell^+\ell^-)$ and$\mathcal{A}_{FB}(B^+_u \to\rho^+\ell^+\ell^-)$ are studied in detail. Ourresults could be used to probe the R-parity violating effects and willcorrelate with searches for the direct R-parity violating signals at the futureexperiments.

The rare decays $B^+_u\to\pi^+\ell^+\ell^-$, $\rho^+\ell^+\ell^-$ and $B^0_d\to \ell^+\ell^-$ in the R-parity violating supersymmetry