The difference in total widths between the $B_c^+$ and $B^+$ mesons is measured using 3.0fb$^{1}$ of data collected by the LHCb experiment in 7 and 8 TeV centreofmass energy protonproton collisions at the LHC. Through the study of the time evolution of $B_c^+ \rightarrow J/\psi \pi^+$ and $B^+\rightarrow J/\psi K^+$ decays, the width difference is measured to be $$ \Delta\Gamma \equiv \Gamma_{B_c^+}  \Gamma_{B^+} = 4.46 \pm 0.14 \pm 0.07mm^{1}c,$$ where the first uncertainty is statistical and the second systematic. The known lifetime of the $B^+$ meson is used to convert this to a precise measurement of the $B_c^+$ lifetime, $$\tau_{B_c^+} = 513.4 \pm 11.0 \pm 5.7fs,$$ where the first uncertainty is statistical and the second systematic.
Invariant mass distributions for (a) selected $ B _ c ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi ^+ $ and (b) $ B ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ $ candidates. The fit result with the function described in the text is shown by the red solid line; the signal (background) components are shown with green (blue) dotted (dashed) lines. 
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(a) Decay time distributions for selected $ B _ c ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi ^+ $ (red solid circles) and $ B ^+ \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ $ (blue open squares) decays, with the data points positioned within the $t$ bins according to Eq. (6) in Ref. [63]; (b) ratio of acceptance functions $\mathcal{R}_{\varepsilon}(ct)$. The uncertainties are due to sample size only. For visualization purposes the efficiency ratio is normalized as $\mathcal{R}_{\varepsilon}(0.5\rm mm /{\mathit{c}})=1$. 
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Ratio of the efficiencycorrected decay time distributions (points with error bars). The curve shows the result of the fit with an exponential function. The data points are positioned within the $t$ bins according to Eq. (6) in Ref. [63]. 
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Animated gif made out of all figures. 
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Summary of systematic uncertainties for $\Delta\Gamma$. 
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Created on 19 February 2021.