  Protons consist of three valence quarks, two up-quarks and one down-quark,
held together by gluons and a sea of quark-antiquark pairs. Collectively,
quarks and gluons are referred to as partons. In a proton-proton collision,
typically only one parton of each proton undergoes a hard scattering - referred
to as single-parton scattering - leaving the remainder of each proton only
slightly disturbed. Here, we report the study of double- and triple-parton
scatterings through the simultaneous production of three J/$\psi$ mesons, which
consist of a charm quark-antiquark pair, in proton-proton collisions recorded
with the CMS experiment at the Large Hadron Collider. We observed this process
- reconstructed through the decays of J/$\psi$ mesons into pairs of oppositely
charged muons - with a statistical significance above five standard deviations.
We measured the inclusive fiducial cross section to be 272 $^{+141}_{-104}$
(stat) $\pm$ 17 (syst) fb, and compared it to theoretical expectations for
triple-J/$\psi$ meson production in single-, double- and triple-parton
scattering scenarios. Assuming factorization of multiple hard-scattering
probabilities in terms of single-parton scattering cross sections, double- and
triple-parton scattering are the dominant contributions for the measured
process.
