Search for $B_c^+\toπ^+μ^+μ^-$ decays and measurement of the branching fraction ratio ${\cal B}(B_c^+\toψ(2S)π^+)/{\cal B}(B_c^+\to J/ψπ^+)$
The first search for nonresonant $B_c^+\toπ^+μ^+μ^-$ 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 ${\cal B}(B_c^+\toπ^+μ^+μ^-)/{\cal B}(B_c^+\to J/ψπ^+) < 2.1\times 10^{-4}$ at $90\%$ confidence level. Additionally, an updated measurement of the ratio of the $B_c^+\toψ(2S)π^+$ and $B_c^+\to J/ψπ^+$ branching fractions is reported. The ratio ${\cal B}(B_c^+\toψ(2S)π^+)/{\cal B}(B_c^+\to J/ψπ^+)$ is measured to be $0.254\pm 0.018 \pm 0.003 \pm 0.005$, 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.