Search for rare $B_{(s)}^0\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ decays

\noindent 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 1.0\ensuremath{{,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 $B_{(s)}^0$ 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 {${\ensuremath{\cal B}\xspace}(\ensuremath{B^0_{s}\rightarrow SP}\xspace) < 1.6 \ (1.2) \times 10^{-8}} and \{{\ensuremath{\cal B}\xspace}(\ensuremath{B^0\rightarrow SP}\xspace)< 6.3 \ (5.1) \times 10^{-9}$} at 95% (90%) confidence level.