# First measurement of the differential branching fraction and $C P$ asymmetry of the $B^\pm\to\pi^\pm\mu^+\mu^-$ decay

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## Abstract

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 proton-proton collision data corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment at centre-of-mass 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.

## Figures and captions

 Feynman diagrams of the penguin and box loop contributions to the $b \rightarrow d \ell^+ \ell^-$ process. feynman.pdf [32 KiB] HiDef png [32 KiB] Thumbnail [17 KiB] *.C file 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. pimumu[..].pdf [20 KiB] HiDef png [340 KiB] Thumbnail [264 KiB] *.C file kmumu_[..].pdf [25 KiB] HiDef png [262 KiB] Thumbnail [198 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 [268 KiB] *.C file piminu[..].pdf [20 KiB] HiDef png [328 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 [446 KiB] Thumbnail [228 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. rho.pdf [14 KiB] HiDef png [109 KiB] Thumbnail [102 KiB] *.C file Animated gif made out of all figures. PAPER-2015-035.gif Thumbnail

## Tables and captions

 The yields of $B ^+ \rightarrow \pi ^+ \mu ^+\mu ^-$ decays in bins of dilepton invariant mass squared, with statistical uncertainties. Table_1.pdf [52 KiB] HiDef png [172 KiB] Thumbnail [83 KiB] tex code 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 [12 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 [66 KiB] tex code

Created on 05 November 2019.