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. 
Fig_1.pdf [143 KiB] HiDef png [207 KiB] Thumbnail [52 KiB] *.C file tex code 

(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 $\mathcal{R}_{\varepsilon}(0.5\rm \,mm /{\mathit{c}})=1$. 
Fig_2.pdf [131 KiB] HiDef png [130 KiB] Thumbnail [42 KiB] *.C file tex code 

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]. 
Fig_3.pdf [51 KiB] HiDef png [119 KiB] Thumbnail [36 KiB] *.C file tex code 

Animated gif made out of all figures. 
PAPER2014060.gif Thumbnail 
Summary of systematic uncertainties for $\Delta\Gamma$. 
Table_1.pdf [62 KiB] HiDef png [73 KiB] Thumbnail [11 KiB] tex code 
Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.