Charm multiplicity distribution in high energy pp collisions with PYTHIA

With the growth of statistics in the future experiments at the LHC, the number of events with charm production will increase substantially. It may become possible to measure the multiplicity distribution of charm particles. Using PYTHIA-8, we generated charm multiplicity distributions in $pp$ collisions for different pseudorapidity ranges ($|η| < 0.5, 1.0, 2.0, 3.0$) and center-of-mass energies ($\sqrt{s}=$ 0.9, 2.36, 2.76, 7.0, 8.0, 13.0 TeV). We investigated the role played by multiple parton interactions and color reconnection. We compared the multiplicity distribution of D mesons with the charm quark multiplicity distribution. We observe that the “quark-hadron” duality hypothesis is satisfied. With the obtained distributions we tested the validity of the Koba-Nielsen-Olesen scaling. We also parameterized the charm distributions considering the Poisson and negative binomial distributions.

💡 Research Summary

In this work the authors present the first systematic study of charm‑particle multiplicity distributions in proton‑proton collisions using the state‑of‑the‑art event generator PYTHIA‑8 (v8.313). They generate 20 million events for each of six centre‑of‑mass energies (√s = 0.9, 2.36, 2.76, 7, 8, 13 TeV) and for four pseudorapidity intervals (|η| < 0.5, 1.0, 2.0, 3.0). Both the partonic charm‑quark multiplicity (counted just before hadronisation) and the hadronic D‑meson multiplicity (including all stable D‑meson species) are recorded, allowing a direct test of the quark‑hadron duality hypothesis.

The study first shows that the D‑meson multiplicity distributions are sharply peaked at low N and fall off over several orders of magnitude. The average multiplicity ⟨N_D⟩ grows slowly with √s and does so at the same rate for all η windows, whereas the charged‑particle multiplicity rises faster and shows a stronger η dependence. This reflects the fact that charm production is a hard process (dominated by g g → c c̄) and is therefore much rarer than the bulk of charged particles.

The role of multiple parton interactions (MPI) and colour reconnection (CR) is investigated by switching these mechanisms on and off. MPI noticeably increases ⟨N_D⟩, especially for the wide η < 3.0 window, indicating that large rapidity intervals are more sensitive to the underlying event activity. In contrast, CR has a negligible effect on charm multiplicities, consistent with the expectation that colour‑string rearrangements mainly affect soft particle production.

A central part of the paper is the test of Koba‑Nielsen‑Olesen (KNO) scaling. By plotting the scaled distribution Ψ(z) = ⟨N_D⟩ P(N_D) versus z = N_D/⟨N_D⟩, the authors find that the curves for different √s overlap only at very low multiplicities; at larger z the distributions separate and develop increasingly long tails with energy. Consequently, strict KNO scaling is violated for charm, with the violation becoming more pronounced as the η window widens. This behaviour mirrors earlier findings for charged particles and points to the growing importance of MPI‑driven fluctuations at high multiplicities.

Finally, the authors fit the simulated multiplicity spectra with three statistical models: a pure Poisson distribution, a single negative binomial distribution (NBD), and a weighted sum of two NBDs. The Poisson description fails because the variance of the data exceeds the mean (over‑dispersion). A single NBD captures the overall shape but underestimates the high‑N tail. The double‑NBD model, interpreted as a superposition of a soft component (low‑N) and a semi‑hard/MPI‑dominated component (high‑N), provides an excellent description across the full multiplicity range. The fitted parameters (means ⟨n₁⟩, ⟨n₂⟩ and dispersion parameters k₁, k₂) increase smoothly with √s and with η, reflecting the growing contribution of multiple hard scatterings.

The paper’s conclusions are threefold: (i) PYTHIA‑8 gives a realistic baseline for future experimental measurements of charm multiplicities at the LHC, especially in the upcoming high‑luminosity runs; (ii) MPI is the dominant driver of the multiplicity increase in wide rapidity intervals, while CR plays a marginal role for charm; (iii) KNO scaling does not hold for charm, indicating that the underlying particle‑production dynamics cannot be reduced to a simple, energy‑independent scaling function. The successful double‑NBD parametrisation offers a compact phenomenological tool for comparing data with theory and for tuning Monte‑Carlo generators. Overall, the work provides a comprehensive framework for interpreting charm‑multiplicity observables and highlights the rich information they can deliver about multi‑parton dynamics in high‑energy hadronic collisions.