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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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 [330 KiB] Thumbnail [268 KiB] *.C file 

piminu[..].pdf [20 KiB] HiDef png [318 KiB] Thumbnail [261 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 [445 KiB] Thumbnail [229 KiB] *.C file 

The $ q^2$ spectrum of $ B ^+ \rightarrow \pi ^+ \mu ^+\mu ^ $ candidates in the region 0.1  1.0 $ {\mathrm{ Ge V^2 /}c^4}$ in a $\pm 50$ $\mathrm{ Me V}$ window around the nominal $ B ^+$ mass, showing a peaking structure at 0.6 $ {\mathrm{ Ge V^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. 
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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 [100 KiB] Thumbnail [52 KiB] tex code 
Created on 06 March 2021.