The differential branching fraction with respect to the dimuon invariant mass squared, and the $C\!P$ asymmetry of the $B^\pm\to\pi^\pm\mu^+\mu^$ decay are measured for the first time. The CKM matrix elements $V_{td}$ and $V_{ts}$, and the ratio $V_{td}/V_{ts}$ are determined. The analysis is performed using protonproton collision data corresponding to an integrated luminosity of 3.0 fb$^{1}$, collected by the LHCb experiment at centreofmass energies of 7 and 8 TeV. The total branching fraction and $C\!P$ asymmetry of $B^\pm\to\pi^\pm\mu^+\mu^$ decays are measured to be \begin{eqnarray} \mathcal{B}(B^\pm\to\pi^\pm\mu^+\mu^) &=& (1.83 \pm 0.24 \pm 0.05) \times 10^{8}\,\,\,\mathrm{and} \nonumber\\ \mathcal{A}_{C\!P}(B^\pm\to\pi^\pm\mu^+\mu^) &=& 0.11 \pm 0.12 \pm 0.01\,, \nonumber \end{eqnarray} where the first uncertainties are statistical and the second are systematic. These are the most precise measurements of these observables to date, and they are compatible with the predictions of the Standard Model.
Feynman diagrams of the penguin and box loop contributions to the $ b \rightarrow d \ell^+ \ell^$ process. 
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The fit to the invariant mass distribution of (left) selected $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ candidates and (right) selected $ B ^+ \!\rightarrow K ^+ \mu ^+\mu ^ $ candidates, with the total model and separate components as described in the legend. 
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kmumu_[..].pdf [25 KiB] HiDef png [262 KiB] Thumbnail [79 KiB] *.C file 

The fit to the invariant mass distribution of (left) selected $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ candidates and (right) selected $ B ^ \rightarrow \pi ^ \mu ^+\mu ^ $ candidates, with the total model and separate components as described in the legend. 
piplus[..].pdf [20 KiB] HiDef png [341 KiB] Thumbnail [106 KiB] *.C file 

piminu[..].pdf [20 KiB] HiDef png [328 KiB] Thumbnail [103 KiB] *.C file 

The differential branching fraction of $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ in bins of dilepton invariant mass squared, $ q^2$ , compared to SM predictions taken from Refs. [1] (APR13), [6] (HKR15) and from lattice QCD calculations [7] (FNAL/MILC15). 
pimumu[..].pdf [20 KiB] HiDef png [446 KiB] Thumbnail [79 KiB] *.C file 

The $ q^2$ spectrum of $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ candidates in the region 0.1  1.0 $ {\mathrm{\,GeV^2\!/}c^4}$ in a $\pm 50$ $\mathrm{\,MeV}$ window around the nominal $ B ^+$ mass, showing a peaking structure at 0.6 $ {\mathrm{\,GeV^2\!/}c^4}$ that is in the region of the $\rho ^0$ and $\omega$ masses squared. 
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Animated gif made out of all figures. 
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The yields of $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ decays in bins of dilepton invariant mass squared, with statistical uncertainties. 
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The measured total yield from the simultaneous fit to the charge separated data, and the inferred yields of $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ and $ B ^ \rightarrow \pi ^ \mu ^+\mu ^ $ decays. 
Table_2.pdf [41 KiB] HiDef png [22 KiB] Thumbnail [4 KiB] tex code 

The results for the differential branching fraction for $ B ^+ \!\rightarrow \pi ^+ \mu ^+\mu ^ $ in bins of $ q^2$ . The first uncertainties are statistical and the second are systematic. 
Table_3.pdf [60 KiB] HiDef png [124 KiB] Thumbnail [22 KiB] tex code 
Created on 15 February 2019.Citation count from INSPIRE on 21 February 2019.