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Prompt double-$$J/\psi $$ production at high-energy hadron colliders can be considered as a golden channel to probe double parton scatterings (DPS)—in particular to study gluon–gluon correlations inside the proton—and, at the same time, to measure the distribution of linearly-polarised gluons inside the proton. Such studies, however, require a good control of both single parton scatterings (SPS) and DPS in the respective regions where they are carried out. In this context, we have critically examined two mechanisms of SPS that may be kinematically enhanced where DPS are thought to be dominant, even though they are either at higher orders in the strong-coupling or velocity expansion. First, we have considered a gauge-invariant and infrared-safe subset of the loop-induced contribution via colour-singlet (CS) transitions. We have found it to become the leading CS SPS contributions at large rapidity separation, yet too small to account for the data without invoking the presence of DPS yields. Second, we have surveyed the possible colour-octet (CO) contributions using both old and up-to-date non-perturbative long-distance matrix elements (LDMEs). We have found that the pure CO yields crucially depend on the LDMEs. Among all the LDMEs we used, only two result into a visible modification of the NRQCD (CS+CO) yield, but only in two kinematical distributions measured by ATLAS, those of the rapidity separation and of the pair invariant mass. These modifications, however, do not impact the control region used for their DPS study.

Prompt $${J/\psi }$$-pair production at the LHC: impact of loop-induced contributions and of the colour-octet mechanism