Measurement of forward $J/\psi$ production cross-sections in $pp$ collisions at $\sqrt{s}=13$ TeV

The production of $J/\psi$ mesons in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV is studied with the LHCb detector. Cross-section 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 cross-sections integrated over the kinematic coverage are $15.30\pm 0.03\pm 0.86$ $\mu$b for prompt $J/\psi$ and $2.34\pm 0.01\pm 0.13$ $\mu$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 cross-section reported for $J/\psi$ mesons from $b$-hadron decays is used to extrapolate to a total $b\bar{b}$ cross-section. The ratios of the cross-sections with respect to $\sqrt{s}=8$ TeV are also determined.