The production of $J/\psi$ mesons in protonproton collisions at a centreofmass energy of $\sqrt{s}=13$ TeV is studied with the \lhcb detector. Crosssection measurements are performed as a function of the transverse momentum $p_\mathrm{T}$ and the rapidity $y$ of the $J/\psi$ meson in the region $p_\mathrm{T}<14\mathrm{GeV}/c$ and $2.0<y<4.5$, for both prompt $J/\psi$ mesons and $J/\psi$ mesons from $b$hadron decays. The production crosssections integrated over the kinematic coverage are $15.03\pm 0.03\pm 0.94$ $\mu$b for prompt $J/\psi$ and $2.25\pm 0.01\pm 0.14$ $\mu$b for $J/\psi$ from $b$hadron decays, assuming zero polarization of the $J/\psi$ meson. The first uncertainties are statistical and the second systematic. The crosssection reported for $J/\psi$ mesons from $b$hadron decays is used to extrapolate to a total $b\bar{b}$ crosssection. The ratios of the crosssections with respect to $\sqrt{s}=8$ TeV are also determined.
Invariant mass (left) and pseudo decay time (right) distributions for the kinematic bin $2< p_{\rm T} <3 {\mathrm{ Ge V /}c} $, $3.0<y<3.5$, with fit results superimposed. The solid (red) line is the total fit function, the shaded (green) area corresponds to the background component. The prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ contribution is shown in crosshatched area (blue), $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ in a solid (black) line and the tail contribution due to the association of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ with the wrong PV is shown in full filled (magenta) area. The tail contribution is not visible in the invariant mass plot. 
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Double differential crosssection for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons as a function of $p_{\rm T}$ in bins of $y$. Statistical and systematic uncertainties are added in quadrature. 
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Double differential crosssection for $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons as a function of $p_{\rm T}$ in bins of $y$. Statistical and systematic uncertainties are added in quadrature. 
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Fractions of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $from$b$ mesons in bins of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ $p_{\rm T}$ and $y$. Statistical and systematic uncertainties are added in quadrature. 
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Differential crosssections as a function of $ p_{\rm T} $ integrated over $y$ for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. 
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Differential crosssections as a function of $y$ integrated over $p_{\rm T}$ for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. 
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Ratios of differential crosssections between measurements at $\sqrt{s}=13\mathrm{ Te V} $ and $\sqrt{s}=8\mathrm{ Te V} $ as a function of $p_{\rm T}$ in bins of $y$ for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. 
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Ratios of differential crosssections between measurements at $\sqrt{s}=13\mathrm{ Te V} $ and $\sqrt{s}=8\mathrm{ Te V} $ as a function of $y$ integrated over $p_{\rm T}$ for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. The FONLL calculation [64] is compared to the measured $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ production ratio. 
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Ratios of differential crosssections between measurements at $\sqrt{s}=13\mathrm{ Te V} $ and $\sqrt{s}=8\mathrm{ Te V} $ as a function of $ p_{\rm T} $ integrated over $y$ for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. Calculations of NRQCD [65] and FONLL [64] are compared to prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons, respectively. 
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The $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ production crosssection for (left) prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and (right) $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons as a function of $pp$ collision energy in the LHCb fiducial region compared to the FONLL calculation [27]. In general, the correlated and uncorrelated systematic uncertainties among different measurements are of comparable magnitude. 
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Differential crosssections as a function of $p_{\rm T}$ integrated over $y$ in the range $2.0<y<4.5$, (left) compared with the NRQCD calculation [65] for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and (right) compared with the FONLL calculation [27] for $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. 
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Animated gif made out of all figures. 
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Relative systematic uncertainties (in %) on the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ crosssection measurements. The uncertainty from the $t_z$ fit only affects $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $from$b$ mesons. Most of the uncertainties are fully correlated between bins, with the exception of the $p_{\rm T}$ , $y$ spectrum dependence and the simulation statistics, which are considered uncorrelated. 
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Double differential production crosssection in $\mathrm{nb}/( {\mathrm{ Ge V /}c} )$ for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons in bins of ($ p_{\rm T} ,y$). The first uncertainties are statistical, the second are the correlated systematic uncertainties shared between bins and the last are the uncorrelated systematic uncertainties. 
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Double differential production crosssection in $\mathrm{nb}/( {\mathrm{ Ge V /}c} )$ for $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} $from$b$ mesons in bins of ($ p_{\rm T} ,y$). The first uncertainties are statistical, the second are the correlated systematic uncertainties shared between bins and the last are the uncorrelated systematic uncertainties. 
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Relative systematic uncertainty (in %) on the ratio of the crosssection in $pp$ collisions at $\sqrt{s}=13 \mathrm{ Te V} $ relative to that at $\sqrt{s}=8\mathrm{ Te V} $. The systematic uncertainty from $t_z$ fits only affects $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \text{from}b$ . 
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Production crosssections of prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons, integrated over the LHCb fiducial region, in $pp$ collisions at various centreofmass energies [12,18,30]. The first uncertainty is the uncorrelated component, and the second the correlated one. 
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The fraction of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons (in %) in bins of the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ transverse momentum and rapidity. The uncertainties are statistical only. The systematic uncertainties are negligible. 
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Differential crosssections $d\sigma/dp_\mathrm{T}$ (in $\mathrm{nb}/( {\mathrm{ Ge V /}c} )$) for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons, integrated over $y$. The first uncertainties are statistical and the second (third) are uncorrelated (correlated) systematic uncertainties amongst bins. 
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Differential crosssections $d\sigma/dy$ (in $ {\rm \upmu b}$ ) for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons, integrated over $p_{\rm T}$ . The first uncertainties are statistical and the second (third) are the uncorrelated (correlated) systematic uncertainties. 
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The ratio of crosssections between measurements at 13 TeV and 8 TeV in different bins of $p_{\rm T}$ and $y$ for prompt $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ mesons. The systematic errors are negligible. 
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The ratio of crosssections between measurements at 13 TeV and 8 TeV in different bins of $p_{\rm T}$ and $y$ for $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu}$ from$b$ mesons. The systematic uncertainties are negligible. 
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The relative increase of the total efficiency (in %), for a $20\%$ polarisation rather than zero, in different bins of $p_{\rm T}$ and $y$. 
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Supplementary material full pdf 
supple[..].pdf [414 KiB] 

This ZIP file contains supplemetary material for the publication LHCbPAPER2015037. The files are: supplementary.pdf : An overview of the extra figures *.C *.pdf, *.png, *.eps : The figures in various formats 
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Created on 20 August 2019.Citation count from INSPIRE on 23 August 2019.