Search for $D^{+}_{(s)} \rightarrow \pi^{+} \mu^{+} \mu^{-}$ and $D^{+}_{(s)} \rightarrow \pi^{-} \mu^{+} \mu^{+}$ decays

A search for non-resonant $D^{+}_{(s)} \rightarrow \pi^{+} \mu^{+} \mu^{-}$ and $D^{+}_{(s)} \rightarrow \pi^{-} \mu^{+} \mu^{+}$ decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, at $\sqrt{s}=7$ TeV recorded by the LHCb experiment in 2011. No signals are observed and the $90\% \, (95\%)$ confidence level (CL) limits on the branching fractions are found to be \begin{eqnarray*} \mathcal{B}(D^{+} \rightarrow \pi^{+} \mu^{+} \mu^{-}) < 7.3 \, (8.3) \times 10^{-8},\\ \mathcal{B}(D^{+}_{s} \rightarrow \pi^{+} \mu^{+} \mu^{-}) < 4.1 \, (4.8) \times 10^{-7},\\ \mathcal{B}(D^{+} \rightarrow \pi^{-} \mu^{+} \mu^{+}) < 2.2 \, (2.5) \times 10^{-8},\\ \mathcal{B}(D^{+}_{s} \rightarrow \pi^{-} \mu^{+} \mu^{+}) < 1.2 \, (1.4) \times 10^{-7}.\\ \end{eqnarray*} These limits are the most stringent to date.