A theoretical preprint estimates that dihadron fragmentation—when a heavy quark produces a pair of quarkonia—can make a significant contribution to quarkonium-pair production, on par with other modeled mechanisms. Independent single fragmentation, by contrast, remains negligible across the modeled kinematic range.
The study asks how single- and dihadron-fragmentation mechanisms contribute to inclusive heavy-quarkonium-pair hadroproduction. Its central comparison is between alternative production mechanisms within a theoretical description of high-energy proton collisions.
The document is an arXiv preprint, arXiv:2608.20329v1 [hep-ph], dated 20 August 2026.
How the calculation works
The framework combines CGC target scattering with analytic dihadron-fragmentation calculations in the heavy-quark mass limit within NRQCD. In practical terms, it links a model of the proton collision with a calculation of how heavy quarks can form paired heavy-quark states.
Within the CGC description, the fragmentation cross section is represented as a convolution of fragmentation functions and dipole-production cross sections. The calculation does not add extra transverse-momentum cuts.
The modeled heavy-flavor contribution includes charm and bottom quarks and assumes separation from the light-quark background. The numerical setup uses the bCGC dipole parameterization, a charm-quark mass of about 1.4 GeV and the HERAPDF20_LO_EIG parton-distribution set.
The stated scale is μ = 2M J/ψ. The expressions are evaluated at leading order, and the scale is varied by a factor of two to examine how sensitive the estimates are to that choice.
The authors also use the relevant light-cone momentum fractions to justify a dilute-dense approximation. In the kinematics they examine, the reported fractions satisfy x1 ≥ 10−1 and x2 ≤ 10−2.
The predicted shape follows the data
When charm and bottom contributions are combined, they are sizable and qualitatively reproduce the observed rapidity-dependence shape. Rapidity describes how the production is distributed along the collision direction, so the comparison concerns the pattern across that distribution rather than a single total value.
The result separates two forms of fragmentation. Independent single fragmentation stays small, while dihadron fragmentation remains significant and comparable with other production mechanisms in the model.
The authors report that these findings remain robust when they vary the renormalization scale, the collinear parton distributions, the forward-dipole parameterization and a conservative invariant-mass cut. That robustness refers to the tested model choices, not to a statistical confidence interval.
A complication for double-parton scattering
The paper’s most consequential claim concerns the relationship between fragmentation and double-parton scattering, or DPS. The authors state that adding their dihadron-fragmentation contribution to direct single-parton scattering, or SPS, would exceed the experimental data.
On that calculation, the data would leave no room for DPS, which describes two separate parton interactions contributing to the same pair-production event. The authors say this would prevent a meaningful extraction of σeff, the parameter used to characterize DPS in this setting.
The conclusion is not a definitive measurement of a DPS contribution or its absence. It is a model-level tension that depends on the ingredients included in the calculation, and the authors suggest that higher-order corrections could reduce it.
What the calculation leaves open
NLO corrections to the fragmentation mechanism were not evaluated. The authors say that such a calculation would require corrections to both fragmentation functions, real-emission effects and multipole-operator modeling.
The analysis also omits interference terms between fragmentation amplitudes. The paper notes that these terms can double the fragmentation contribution in some regions, making them a potentially important source of change in the predicted total.
The conclusions therefore remain tied to the chosen leading-order framework, dipole parameterization, parton distributions, scale choices and invariant-mass treatment. The study tests variations of several of those inputs, but it does not calculate the missing higher-order effects.
The calculation is focused on heavy-flavor contributions from charm and bottom, with the light-quark background treated as separate. Its results should consequently be read as predictions for the stated heavy-flavor and kinematic setup, rather than as a complete account of every possible fragmentation channel.
The next test is a fuller calculation
A calculation including NLO corrections, real emissions, multipole-operator effects and the omitted interference terms would show whether the excess over the data survives. It would also clarify whether a quantitative DPS contribution and a meaningful σeff extraction remain possible.
For now, the preprint’s main contribution is to place dihadron fragmentation alongside the mechanisms that must be considered when quarkonium-pair yields are interpreted. Its conclusion is that single fragmentation is a small correction, while dihadron fragmentation is a substantial component of the modeled production picture.
The research was partially supported by Proyecto ANID PIA/APOYO AFB220004, ANID Fondecyt Regular Grants 1251322 and 1251975, and NLHPC supercomputing infrastructure ECM-02. The full FeynCalc-generated charm expressions are not printed, although the authors state that they can be supplied on demand as C/C++ code.
Paper data and sources
Original title: Production of quarkonium pairs via the fragmentation mechanism
Authors: Franco Barattini, Benjamin Guiot, Marat Siddikov
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text