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Measurement of the $J/\psi$ pair production cross-section in $pp$ collisions at $\sqrt{s} = 13 \,{\mathrm{TeV}}$

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Abstract

The production cross-section of $J/\psi$ pairs is measured using a data sample of $pp$ collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13 \,{\mathrm{TeV}}$, corresponding to an integrated luminosity of $279 \pm 11 \,{\mathrm{pb^{-1}}}$. The measurement is performed for $J/\psi$ mesons with a transverse momentum of less than $10 \,{\mathrm{GeV}}/c$ in the rapidity range $2.0<y<4.5$. The production cross-section is measured to be $15.2 \pm 1.0 \pm 0.9 \,{\mathrm{nb}}$. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the $J/\psi$ pair are measured and compared to theoretical predictions.

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Projections of the fit to the efficiency-corrected distribution of the reconstructed $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $ mass for (left) $M(\mu^+_1\mu^-_1)$ and (right) $M(\mu^+_2\mu^-_2)$. The (black) points with error bars represent the data. The (blue) solid line is the total fit function. The (red) cross-hatched area shows the signal distribution. The (black and magenta) dashed lines represent the background components due to the combination of a real $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $ with a combinatorial candidate. The (green) shaded area shows the purely combinatorial background.

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Comparisons between measurements and theoretical predictions for the differential cross-sections as a function of $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions for the differential cross-sections as functions of (top left) $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$, (top right) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ and (bottom) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions for the differential cross-sections as functions of (top left) $\left| \Delta y \right|$, (top right) $\left| \Delta \phi \right|$, (bottom left) $\mathcal{A}_{\mathrm{T}}$ and (bottom right) $m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions with $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>1 {\mathrm{\,GeV\!/}c} $ for the differential cross-sections as functions of (top left) $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$, (top right) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ and (bottom) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions with $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>1 {\mathrm{\,GeV\!/}c} $ for the differential cross-sections as functions of (top left) $\left| \Delta y \right|$, (top right) $\left| \Delta \phi \right|$, (bottom left) $\mathcal{A}_{\mathrm{T}}$ and (bottom right) $m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions with $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>3 {\mathrm{\,GeV\!/}c} $ for the differential cross-sections as functions of (top left) $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$, (top right) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ and (bottom) $y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Comparisons between measurements and theoretical predictions with $p_{\mathrm{T}}( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>3 {\mathrm{\,GeV\!/}c} $ for the differential cross-sections as functions of (top left) $\left| \Delta y \right|$, (top right) $\left| \Delta \phi \right|$, (bottom left) $\mathcal{A}_{\mathrm{T}}$ and (bottom right) $m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$. The (black) points with error bars represent the measurements.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} p_{\mathrm{ T}} ( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$ and $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} \left| \Delta y \right|}$. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$ and $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$ for the $ p_{\mathrm{ T}} ( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>1 {\mathrm{\,GeV\!/}c} $ region. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} \left| \Delta y \right|}$ for the $ p_{\mathrm{ T}} ( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>1 {\mathrm{\,GeV\!/}c} $ region. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} y( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$ and $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} m( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}$ for the $ p_{\mathrm{ T}} ( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>3 {\mathrm{\,GeV\!/}c} $ region. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Result of templated DPS fit for $\frac{ \mathrm{d}\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{\mathrm{d} \left| \Delta y \right|}$ for the $ p_{\mathrm{ T}} ( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )>3 {\mathrm{\,GeV\!/}c} $ region. The (black) points with error bars represent the data. The total fit result is shown with the thick (red) solid line and the DPS component is shown with the thin (orange) solid line.

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Tables and captions

Summary of the systematic uncertainties on the measurement of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $ pair production cross-section.

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Summary of the theoretical predictions and the measurement of $\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$ for different regions of transverse momentum of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $ pair. For SPS predictions, the first uncertainty accounts for the variation of PDFs and gluon densities, while the second one corresponds to the variation of the factorisation and renormalisation scales. For the LO CO predictions the third uncertainty corresponds to the choice of LDMEs from Refs. [25,114,115,116,117,118,119,120]. For NLO CS predictions [39] the uncertainty corresponds to the variation of the factorisation and renormalization scales. For the DPS prediction the first uncertainty is due to the measured prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ production cross-section [86] and the second is due to the uncertainty in $\sigma_{\mathrm{eff}}$ [44,92].

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Percentages of the DPS component, $f_{\mathrm{DPS}}$, determined with the simple twodash-component fit to different distributions for different SPS models.

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Summary of the $\sigma_{\mathrm{eff}}$ values (in ${\mathrm{mb}} $) from DPS fits for different SPS models. The uncertainty is statistical only, originating from the statistical uncertainty in $\sigma_{\mathrm{DPS}}$ (and ${\mathrm{d}\sigma\left( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \right)}/{\mathrm{d}v}$). The common systematic uncertainty of 12%, accounting for the systematic uncertainty of $\sigma\left( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \right)$ and the total uncertainty for $\sigma( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )$, is not shown.

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Supplementary Material [file]

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Created on 09 December 2018.Citation count from INSPIRE on 09 December 2018.