In high-energy hadron–hadron collisions, each incoming hadron behaves as a loosely bound system of massless partons – quarks, antiquarks and gluons. The interaction of incoming hadrons is described as the pair-wise interactions of partons from one incoming hadron with partons from the other hadron. This model agrees well with numerous precise experimental data, in particular with the production of heavy-flavoured particles. Such processes have been studied at the Tevatron and at the LHC. All experimental data agree well with the dominant contribution coming from the single pair-wise collision of gluons, producing a single charm–anticharm (cc) or bottom–antibottom (bb) pair, the so-called single parton scattering (SPS) paradigm. However, evidence for the production of multiple cc pairs in single hadron–hadron collisions has been reported by the NA3 and WA75 collaborations, who observed J/ψJ/ψ pairs, and three charmed mesons, respectively. Also, Bc meson production requires a cc and a bb pair. Yet these processes are consistent with a SPS of gluons.

At higher energy, the probability of a second hard parton interaction becomes non-negligible. The evidence for this kind of process, named double parton scattering (DPS), was obtained a long time ago by the AFS and UA2 collaborations. At the LHC where the energies of colliding protons are much larger, the DPS contribution is expected to be more prominent, and even dominant for some processes.

Assuming the independence of partons, the rate of DPS processes is proportional to a product of the independent rates for two pair-wise parton collisions. A consequence is that the corresponding proportionality coefficient is universal, independent of the collision energy, and of the considered process. The inverse of this proportionality coefficient has the dimension of an area and is named the "effective DPS cross-section", σeff.

The significant role of DPS processes at the LHC has been demonstrated by the LHCb collaboration via the measurement of the simultaneous production of J/ψ mesons and charm hadrons. The measured rates are found to be 30 times larger than predicted from the SPS paradigm and in agreement with DPS predictions, showing the dominance of the DPS contribution in these processes. The measured parameter σeff is found to be in excellent agreement with those determined by the CDF collaboration from the study of jet events, but significantly more precise.

Recently, LHCb has extended this analysis to studying the simultaneous production of Υ mesons and charm hadrons. Such final states rely on the simultaneous production of cc and bb pairs. The full Run 1 data set has been used in this analysis.

The measured production rates exceed significantly the theory predictions, based on the SPS approach, but agree nicely with the DPS paradigm.

The measured parameter σeff is in very good agreement with all previous determinations and within the most precise measurements of this important parameter. The current best measurements of the σeff parameter are summarised in the figure.