Observation of triple $\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi$ meson production in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$

The first observation of the combined production of three $\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi$ mesons in proton-proton collisions at a center-of-mass energy of $13\,\mathrm{TeV}$ is reported. The analysis is based on a data sample recorded by the CMS experiment at the CERN LHC corresponding to an integrated luminosity of $133\,\mathrm{fb}^{-1}$. The search for triple-$\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi$ production is performed in final states with three $\mu^{+}\mu^{-}$ pairs that pass fiducial kinematic criteria chosen so as to select high-$p_\mathrm{T}$ $\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi$ mesons produced at midrapidity. The $\mathrm{pp}\to\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{X}$ process is observed with a significance in excess of five standard deviations. The fiducial cross section for this process is found to be $\sigma(\mathrm{pp}\to\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi\,\mathrm{X})= 272^{+141}_{-104} \mathrm{(stat)} \pm 17 \mathrm{(syst)} \,\mathrm{fb}$. The result is compared to theoretical expectations for the production of three $\mathrm{J}\mspace{-2mu}/\mspace{-2mu}\psi$ mesons in single (SPS), double- (DPS), and triple- (TPS) parton scattering processes. Under the most economical assumption of factorization of multiple hard scattering probabilities in terms of SPS cross sections, the measured final state is found to be dominated by DPS and TPS contributions. A value of the associated DPS effective cross section parameter of $\sigma_\mathrm{eff,DPS} = 2.7 ^{+1.4}_{-1.0} \mathrm{(exp)} ^{+1.5}_{-1.0}\mathrm{(theo)}\,\mathrm{mb}$, related to the transverse distribution of partons in the proton, is derived.