Measurement of $J/\psi$-pair production in $pp$ collisions at $\sqrt{s}=13$ TeV and study of gluon transverse-momentum dependent PDFs

Information

LHCb-PAPER-2023-022
CERN-EP-2023-242
arXiv:2311.14085 [PDF]

(Submitted on 23 Nov 2023)
JHEP 03 (2024) 088
Inspire 2725992

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Abstract

The production cross-section of $J/\psi$ pairs in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV is measured using a data sample corresponding to an integrated luminosity of 4.2 fb$^{-1}$ collected by the LHCb experiment. The measurement is performed with both $J/\psi$ mesons in the transverse momentum range $0<p_{\text{T}}<14$ GeV/$c$ and rapidity range $2.0<y<4.5$. The cross-section of this process is measured to be 16.36$\pm$0.28(stat)$\pm$0.88(syst) nb. The contributions from single-parton scattering and double-parton scattering are separated based on the dependence of the cross-section on the absolute rapidity difference $\Delta y$ between the two $J/\psi$ mesons. The effective cross-section of double-parton scattering is measured to be $\sigma_{\text{eff}}=$13.1$\pm$1.8(stat)$\pm$2.3(syst) mb. The distribution of the azimuthal angle $\phi_{\text{CS}}$ of one of the $J/\psi$ mesons in the Collins-Soper frame and the $p_{\text{T}}$-spectrum of the $J/\psi$ pairs are also measured for the study of the gluon transverse-momentum dependent distributions inside protons. The extracted values of $\langle\cos2\phi_{\text{CS}}\rangle$ and $\langle\cos4\phi_{\text{CS}}\rangle$ are consistent with zero, but the presence of azimuthal asymmetry at a few percent level is allowed.

Figures and captions

Invariant mass distributions of two $\mu ^+\mu ^- $ pairs (a) $m_{\mu_1^+\mu_1^-}$ and (b) $m_{\mu_2^+\mu_2^-}$ for di- $ { J \mskip -3mu/\mskip -2mu\psi }$ candidates together with the projections of the two-dimensional fit.	Fig1a.pdf [27 KiB] HiDef png [297 KiB] Thumbnail [251 KiB] *.C file
	Fig1b.pdf [25 KiB] HiDef png [255 KiB] Thumbnail [210 KiB] *.C file
Distributions of (a) $t_z^{ { J \mskip -3mu/\mskip -2mu\psi } _1}$ and (b) $t_z^{ { J \mskip -3mu/\mskip -2mu\psi } _2}$ for di- $ { J \mskip -3mu/\mskip -2mu\psi }$ signals with backgrounds subtracted. The projections of the fit result are overlaid.	Fig2a.pdf [19 KiB] HiDef png [256 KiB] Thumbnail [197 KiB] *.C file
	Fig2b.pdf [20 KiB] HiDef png [309 KiB] Thumbnail [248 KiB] *.C file
Differential cross-section of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production for SPS+DPS, DPS and SPS as a function of (a) $\Delta y$, (b) $\Delta\phi$, (c) $\mathcal{A}_{ p_{\mathrm{T}} }$, (d) $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (e) $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (f) $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (g) $ p_{\mathrm{T}} ^{ { J \mskip -3mu/\mskip -2mu\psi } }$ and (h) $y_{ { J \mskip -3mu/\mskip -2mu\psi } }$. The error bars represent the statistical and systematic uncertainties added in quadrature. The purple dashed lines in (a) and (c) indicate the baseline of zero.	Fig3a.pdf [12 KiB] HiDef png [148 KiB] Thumbnail [142 KiB] *.C file
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Summary of $\sigma_{\text{eff}}$ measurements in $pp$ or $ p \overline p $ collisions [29,30,31,32,33,34,35,36,37,38,39,40,41,42]. The legend entries marked with an asterisk are taken from a third-party calculation based on the original experimental result [28,70,71,72,73].	Fig4.pdf [14 KiB] HiDef png [350 KiB] Thumbnail [367 KiB] *.C file
Differential cross-section of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production for SPS+DPS and SPS as a function of (a) $\Delta y$, (b) $\Delta\phi$, (c) $\mathcal{A}_{ p_{\mathrm{T}} }$, (d) $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (e) $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (f) $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$, (g) $ p_{\mathrm{T}} ^{ { J \mskip -3mu/\mskip -2mu\psi } }$ and (h) $y_{ { J \mskip -3mu/\mskip -2mu\psi } }$, compared with the NLO* CS predictions for SPS [74,75,76]. The $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ spectrum is also compared with the PRA+NRQCD predictions for SPS [77].	Fig5a.pdf [15 KiB] HiDef png [550 KiB] Thumbnail [319 KiB] *.C file
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Differential cross-section of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production for SPS+DPS and SPS as a function of $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ for candidates with $9<m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }<24\text{ Ge V /}c^2 $, compared with the PRA+NRQCD predictions for SPS [77].	Fig6.pdf [16 KiB] HiDef png [379 KiB] Thumbnail [243 KiB] *.C file
Distribution of $\phi_{\text{CS}}$ (a) with the SPS and DPS contributions separated in the TMD region $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }<4.1\text{ Ge V /}c $ and (b) for SPS with the function described in the text overlaid. The systematic uncertainties correlated between intervals are excluded from the error bars.	Fig7a.pdf [14 KiB] HiDef png [151 KiB] Thumbnail [149 KiB] *.C file
	Fig7b.pdf [13 KiB] HiDef png [164 KiB] Thumbnail [137 KiB] *.C file
Normalised $ p_{\mathrm{T}}$ spectrum of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in different $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ intervals, compared with TMD predictions [18] in the TMD region $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }<\langle m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }\rangle/2$. The average values of the $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ distributions in three $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ intervals are presented at the top of the figure.	Fig8.pdf [16 KiB] HiDef png [360 KiB] Thumbnail [289 KiB] *.C file
Normalised $ p_{\mathrm{T}}$ spectrum of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in three $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ intervals with $\langle m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }\rangle=$6.6, 7.9 and 11.0 $\text{ Ge V /}c^2$ , compared with TMD predictions [18] in the TMD region $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }<\langle m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }\rangle/2$. The average values of the $ p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ distributions in three $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ intervals are presented at the top of the figure.	Fig9.pdf [16 KiB] HiDef png [445 KiB] Thumbnail [349 KiB] *.C file
Animated gif made out of all figures.	PAPER-2023-022.gif Thumbnail

Tables and captions

Summary of the systematic uncertainties on the measurement of the di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production cross-section. The total systematic uncertainty is a quadratic sum of these uncertainties.	Table_1.pdf [35 KiB] HiDef png [103 KiB] Thumbnail [46 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\Delta y$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_2.pdf [44 KiB] HiDef png [212 KiB] Thumbnail [71 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\Delta\phi$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_3.pdf [44 KiB] HiDef png [225 KiB] Thumbnail [90 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\mathcal{A}_{ p_{\mathrm{T}} }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_4.pdf [58 KiB] HiDef png [203 KiB] Thumbnail [63 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_5.pdf [60 KiB] HiDef png [147 KiB] Thumbnail [73 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_6.pdf [59 KiB] HiDef png [217 KiB] Thumbnail [94 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_7.pdf [60 KiB] HiDef png [136 KiB] Thumbnail [61 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{ { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_8.pdf [59 KiB] HiDef png [174 KiB] Thumbnail [83 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} y_{ { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production. The first uncertainties are statistical, and the second systematic.	Table_9.pdf [51 KiB] HiDef png [228 KiB] Thumbnail [101 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\Delta y$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_10.pdf [44 KiB] HiDef png [217 KiB] Thumbnail [101 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\Delta\phi$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_11.pdf [44 KiB] HiDef png [229 KiB] Thumbnail [91 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d}\mathcal{A}_{ p_{\mathrm{T}} }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_12.pdf [58 KiB] HiDef png [193 KiB] Thumbnail [63 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_13.pdf [60 KiB] HiDef png [148 KiB] Thumbnail [74 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_14.pdf [59 KiB] HiDef png [233 KiB] Thumbnail [103 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_15.pdf [60 KiB] HiDef png [133 KiB] Thumbnail [60 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{ { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_16.pdf [59 KiB] HiDef png [170 KiB] Thumbnail [82 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} y_{ { J \mskip -3mu/\mskip -2mu\psi } }$ of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS. The first uncertainties are statistical, and the second systematic.	Table_17.pdf [51 KiB] HiDef png [225 KiB] Thumbnail [101 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [nb/( $\text{Ge V /}c$ )] of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in intervals of $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$. The first uncertainties are statistical, and the second systematic.	Table_18.pdf [59 KiB] HiDef png [124 KiB] Thumbnail [57 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [nb/( $\text{Ge V /}c$ )] of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS in intervals of $y_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$. The first uncertainties are statistical, and the second systematic.	Table_19.pdf [59 KiB] HiDef png [124 KiB] Thumbnail [57 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [nb/( $\text{Ge V /}c$ )] of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in intervals of $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [ $\text{Ge V /}c^2$ ]. The first uncertainties are statistical, and the second systematic.	Table_20.pdf [59 KiB] HiDef png [114 KiB] Thumbnail [50 KiB] tex code
Differential cross-sections $\mathrm{d}\sigma/\mathrm{d} p_{\mathrm{T}} ^{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [nb/( $\text{Ge V /}c$ )] of di- $ { J \mskip -3mu/\mskip -2mu\psi }$ production in SPS in intervals of $m_{\text{di-} { J \mskip -3mu/\mskip -2mu\psi } }$ [ $\text{Ge V /}c^2$ ]. The first uncertainties are statistical, and the second systematic.	Table_21.pdf [59 KiB] HiDef png [115 KiB] Thumbnail [50 KiB] tex code