A discovery of the rare decay $B^{+} \rightarrow \pi^{+} \mu^{+} \mu^{}$ is presented. This decay is observed for the first time, with 5.2 $\sigma$ significance. The observation is made using $pp$ collision data, corresponding to an integrated luminosity of 1.0 fb$^{1}$, collected with the LHCb detector. The measured branching fraction is (2.3 $\pm$ 0.6 (stat.) $\pm$ 0.1 (syst.))$\times 10^{8}$, and the ratio of the $B^{+} \rightarrow \pi^{+} \mu^{+} \mu^{}$ and $B^{+} \rightarrow \K^{+} \mu^{+} \mu^{}$ branching fractions is measured to be 0.053 $\pm$ 0.014 (stat.) $\pm$ 0.001 (syst.).
BDT output distribution for simulated $ B ^+ \rightarrow \pi ^+ \mu ^+ \mu ^ $ events (black solid line) and candidates taken from the mass sidebands in the data (red dotted line). Both distributions are normalised to unit area. The vertical line indicates the chosen cut value of 0.325. 
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Invariant mass distribution for $ B ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ $ candidates under the (a) $ K ^+ \mu ^+ \mu ^ $ and (b) $\pi ^+ \mu ^+ \mu ^ $ mass hypotheses with the fit projections overlaid. In the legend, "part. reco" refers to partially reconstructed background. The fit models are described in the text. 
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Invariant mass distribution of $ B ^+ \rightarrow \pi ^+ \mu ^+ \mu ^ $ candidates with the fit projection overlaid (a) in the full mass range and (b) in the region around the $ B $ mass. In the legend, "part. reco." and "combinatorial" refer to partially reconstructed and combinatorial backgrounds respectively. The discontinuity at 5500 $ {\mathrm{ Me V /}c^2}$ is due to the removal of data used for training the BDT. 
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Invariant mass distribution of $ B ^+ \rightarrow K ^+ \mu ^+ \mu ^ $ candidates with the fit projection overlaid (a) in the full mass range and (b) in the region around the $ B $ mass. In the legend, "combinatorial" refers to the combinatorial background. 
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kmumuf[..].pdf [18 KiB] HiDef png [203 KiB] Thumbnail [159 KiB] *.C file 

Invariant mass distribution of ${B^+\rightarrow J / \psi \pi ^+ }$ candidates with the fit projection overlaid. In the legend, "part. reco." and "combinatorial" refer to partially reconstructed and combinatorial backgrounds respectively. The fit model is described in the text. 
jpsipifit.pdf [32 KiB] HiDef png [227 KiB] Thumbnail [186 KiB] *.C file 

Animated gif made out of all figures. 
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Summary of systematic uncertainties. 
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Created on 20 February 2021.