The search for $B_c^+ \rightarrow \pi^{+}\mu^{+}\mu^{-}$ and updating the measurement $\mathcal{B}(B_c^+\rightarrow\psi (2S) \pi^{+})/\mathcal{B}( B_c^+ \rightarrow J/ \psi \pi^{+})$ with the LHCb experiment

We perform a search for non-resonant $B_c^+ \rightarrow \pi^{+}\mu^{+}\mu^{-}$ decays. We reconstruct $B_c^+ \rightarrow \pi^{+}\mu^{+}\mu^{-}$ decays and use the invariant mass of the $ B_c^+ $ candidates as discriminating observable to search for a signal using extended, unbinned maximum likelihood fit in dimuon mass. The signal yield, normalized to the yield of reconstructed $B_c^+ J/ \psi (\mu^{+}\mu^{-}) \pi^{+}$ decays, is used to obtain a result on the relative branching fractions. As no significant signal for non-resonant decays is seen, we provide a limit for the ratio of branching fractions, $\mathcal{B}( B_c^+\rightarrow\pi^{+}\mu^{+}\mu^{-}/\mathcal{B}(B_c^+\rightarrow J/\psi\pi^{+})$. We also provide an update on the ratio of branching fractions $\mathcal{B}(B_c^+\rightarrow\psi(2S)\pi^{+})/\mathcal{B}(B_c^+\rightarrow J/\psi\pi^{+})$.