Search for $${{B} _{c} ^+} \!\rightarrow {{\pi } ^+} {\mu ^+\mu ^-} $$ decays and measurement of the branching fraction ratio $${\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {\psi {(2S)}} {{\pi } ^+} )/{\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\pi } ^+} )$$

The first search for nonresonant B+ c → π+μ+μ− decays is reported. The analysis uses proton–proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 fb−1. No evidence for an excess of signal events over background is observed and an upper limit is set on the branching fraction ratio B(B+ c → π+μ+μ−)/B(B+ c → J/ψπ+) < 2.1×10−4 at 90% confidence level. Additionally, an updated measurement of the ratio of the B+ c → ψ(2S)π+ and B+ c → J/ψπ+ branching fractions is reported. The ratio B(B+ c → ψ(2S)π+)/B(B+ c → J/ψπ+) is measured to be 0.254 ± 0.018 ± 0.003 ± 0.005, where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the leptonic J/ψ and ψ(2S) decays. This measurement is the most precise to date and is consistent with previous LHCb results