The lifetime of the $B_c^+$ meson is measured using semileptonic decays having a $J / \psi$ meson and a muon in the final state. The data, corresponding to an integrated luminosity of $2\mathrm{ fb^{1}}$, are collected by the LHCb detector in $pp$ collisions at a centreofmass energy of $8 \mathrm{TeV}$. The measured lifetime is $$\tau = 509 \pm 8 \pm 12 \mathrm{ fs},$$ where the first uncertainty is statistical and the second is systematic.
Distributions of $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ , without simulation of detector response, for the Kiselev (red solid line), Ebert (green shortdashed line), and ISGW2 (black longdashed line) models. 
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Corrections to the (a) $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ and (b) $k$factor model due to the contribution of feeddown modes after the selection. The contribution to the $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ distribution from $ B _ c ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu ^+ \nu _\mu $ decays alone is shown by the black solid curve, while the inclusion of each modelled feeddown contribution is shown by the shaded areas according to the legend. The mean and r.m.s. width of the $k$factor distribution are shown as a function of $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ before (solid line) and after (dashed line) the inclusion of feeddown modes. 
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Result of a fit in the ($\mathrm{DLL} _{p/\pi}, \mathrm{DLL} _{K/\pi}$) plane to determine the fractions of hadron species in the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ track sample. The colour of each bin is built as a combination of red, green and blue proportional to the fitted fractions of pions, kaons and protons, respectively. 
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Dimuon mass distribution for the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ candidates. The selected signal region is shown by the central lightshaded area. The sidebands used for the estimation of the fake $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ background are shown by the darkshaded areas, and the function modelling such background by the solid red curve. 
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Result of the twodimensional fit of the $ B _ c ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu ^+ \nu _\mu X$ model. Projections of the total fit function and its components are shown for (a) the pseudoproper time , (b) the mass of all events, and (c) the mass of the detached events ($ t_{\mathrm{ps}} > 150$ fs). 
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Binned distributions of (a) $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ , and (b,c) the two $q^2$ solutions for events in the detached region. The modelled contributions for misidentification background (hatched dark violet), fake $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ background (filled light green), combinatorial background (hatched light orange) and signal (filled dark red), are shown, stacked on each other. Markers representing data are superimposed. The background yields and {PDF }s are obtained with the techniques described in Sec. 5, and only the signal yield is obtained from the fit to the data. 
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Effect of a generic deformation of the signal model: (a) offset to the lifetime value (expressed in fs) as a function of the deformation parameters; (b) fit projection for the $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ variable in the detached region after applying the deformation maximising the agreement with data ($\alpha_\psi = \alpha_\nu$ = 0.3 $c^2\mathrm{ Ge V} ^{1}$). The colour scale on the upper plot indicates the $p$value of the goodnessoffit test on the three decay kinematic distributions. The solid blue (dashed red) lines shows the region having $p$value greater than 32% for the $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ ($q^2$) test only. The filled (empty) blue marker indicates the deformation parameters that fit best the Ebert (ISGW2) model. The fit components shown on the lower plot follow the legend of Fig. 6. 
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Lifetime results obtained after reducing the range of the $ t_{\mathrm{ps}}$ and $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ variables (a) removing the events with $ t_{\mathrm{ps}}$ lower than the threshold reported on the $x$axis and, (b) dividing events in bins of $ M_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \mu}$ . The dark (light) shaded band on (a) shows the expected $\pm$1(2) statistical standard deviation ($\sigma$) of the lifetime variation due to the reduced sample size. The horizontal line on (b) shows the lifetime result of the nominal fit. 
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Animated gif made out of all figures. 
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Systematic uncertainties on the $ B _ c ^+$ lifetime. 
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File LHCbPAPER2013063supplementary.zip contains the following figures: SupplementaryFig1 : Comparison of the result of this determination of the B_c^+ meson lifetime with those from previous measurements SupplementaryFig2a : Result of the twodimensional fit of the B_c^+ > J/psi mu^+ nu X model  Time projection SupplementaryFig2b : Result of the twodimensional fit of the B_c^+ > J/psi mu^+ nu X model  Mass projection SupplementaryFig2c : Result of the twodimensional fit of the B_c^+ > J/psi mu^+ nu X model  Mass projection for t_ps > 150 fs SupplementaryFig3 : Mass projection of the model for t_ps > 150 fs after applying a signal deformation which maximise compatibility with data 
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Created on 18 October 2019.