Measurement of associated $J\mathrm{/}\psi$-$\psi (2S)$ production cross-section in $pp$ collisions at $\sqrt{s}=13$ TeV

The cross-section of associated $J\mathrm{/}\psi$-$\psi (2S)$ production 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 for both $J\mathrm{/}\psi$ and $\psi (2S)$ mesons having transverse momentum $p_{\text{T}}<14$ GeV/$c$ and rapidity $2.0<y<4.5$, assuming negligible polarisation of the $J\mathrm{/}\psi$ and $\psi (2S)$ mesons. The production cross-section is measured to be $4.5\pm 0.7\pm 0.3$ nb, where the first uncertainty is statistical and the second systematic. The differential cross-sections are measured as functions of several kinematic variables of the $J\mathrm{/}\psi$-$\psi (2S)$ candidates. The results are combined with a measurement of $J\mathrm{/}\psi$-$J\mathrm{/}\psi$ production, giving a cross-section ratio between $J\mathrm{/}\psi$-$\psi (2S)$ and $J\mathrm{/}\psi$-$J\mathrm{/}\psi$ production of $0.274\pm 0.044\pm 0.008$, where the first uncertainty is statistical and the second systematic.