oindent A search for the decays $B^0_{s}rightarrow mu^+ mu^- mu^+ mu^-$ and $B^0 rightarrow mu^+ mu^- mu^+ mu^-$ is performed using data, corresponding to an integrated luminosity of 1.0ensuremath{{,fb}^{-1}}xspace, collected with the LHCb detector in 2011. The number of candidates observed is consistent with the expected background and, assuming phase-space models of the decays, limits on the branching fractions are set: {${ensuremath{cal B}xspace}(B^0_{s}rightarrow mu^+ mu^- mu^+ mu^-) < 1.6 (1.2) times 10^{-8}$} and {${ensuremath{cal B}xspace}(B^0 rightarrow mu^+ mu^- mu^+ mu^-)< 6.6 (5.3) times 10^{-9}$} at 95,% (90,%) confidence level. In addition, limits are set in the context of a supersymmetric model which allows for the $B^0_{(s)}$ meson to decay into a scalar ($S$) and pseudoscalar particle ($P$), where $S$ and $P$ have masses of 2.5 GeV and 214.3 MeV, respectively, both resonances decay into $mu^+mu^-$. The branching fraction limits for these decays are {${ensuremath{cal B}xspace}(ensuremath{B^0_{s}rightarrow SP}xspace) < 1.6 (1.2) times 10^{-8}$} and {${ensuremath{cal B}xspace}(ensuremath{B^0rightarrow SP}xspace)< 6.3 (5.1) times 10^{-9}$} at 95% (90%) confidence level.
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