Measurement of $J/ψ$-pair production in $pp$ collisions at $\sqrt{s}=13$ TeV and study of gluon transverse-momentum dependent PDFs
The production cross-section of $J/ψ$ 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 $J/ψ$ 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 $Δy$ between the two $J/ψ$ mesons. The effective cross-section of double-parton scattering is measured to be $σ_{\text{eff}}=$13.1$\pm$1.8(stat)$\pm$2.3(syst) mb. The distribution of the azimuthal angle $ϕ_{\text{CS}}$ of one of the $J/ψ$ mesons in the Collins-Soper frame and the $p_{\text{T}}$-spectrum of the $J/ψ$ pairs are also measured for the study of the gluon transverse-momentum dependent distributions inside protons. The extracted values of $\langle\cos2ϕ_{\text{CS}}\rangle$ and $\langle\cos4ϕ_{\text{CS}}\rangle$ are consistent with zero, but the presence of azimuthal asymmetry at a few percent level is allowed.