A study of charged-particle multiplicity distribution in high energy p-O collisions

This study investigates the multiplicity distribution of charged particles generated in $p$-O collisions, employing Pythia (Angantyr) and $k_T$-factorization approach. Oxygen nucleus configurations are sampled using a $α$-cluster model to evaluate both formalisms and assess how initial nucleus configuration influences the properties of the produced final states. Results obtained through clustering are systematically compared to those derived from the Woods-Saxon nuclear distribution. The analysis encompasses various pseudorapidity intervals ($|η|<$ 0.5, 1.0, 2.0, 3.0) and center-of-mass energies ($\sqrt{s}=$ 2.36, 5.02, 7.0, 13.0 TeV). Based on the resulting distributions, we examine the KNO scaling effect and fit the distributions with the double NBD model for parameterization, aiming to accurately characterize the observed results and elucidate contributions from both soft and semi-hard processes. Our results indicate that different geometric descriptions of the oxygen nucleus project significantly different multiplicities of charged particles, especially for large multiplicities and higher pseudorapidity. We also observed that multiplicity of charged particles calculated with Pythia reveals significantly different behavior from that calculated with $k_T$-factorization.

💡 Research Summary

This paper presents a comprehensive study of charged‑particle multiplicity distributions in high‑energy proton‑oxygen (p‑O) collisions, focusing on how the geometric description of the oxygen nucleus influences final‑state observables. Two fundamentally different theoretical frameworks are employed: the Monte‑Carlo event generator Pythia 8.313 with its Angantyr model, and a small‑x Color Glass Condensate (CGC) based kₜ‑factorization approach. Both frameworks are applied to the same set of collision energies (√s = 2.36, 5.02, 7.0, 13 TeV) and four pseudorapidity windows (|η| < 0.5, 1.0, 2.0, 3.0).

The nuclear geometry is modeled in two ways. In the traditional Woods‑Saxon picture, nucleons are distributed according to a smooth, spherical density profile. In the alternative α‑cluster model, the ¹⁶O nucleus is built from four α‑particles placed at the vertices of a regular tetrahedron; each α‑cluster’s internal nucleon distribution follows a three‑parameter Fermi (3pF) function (R = 0.964 fm, a = 0.322 fm, w = 0.517) to reproduce realistic central curvature. This construction yields a highly inhomogeneous initial condition with localized high‑density spots.

Within Pythia/Angantyr, the collision is treated using a Glauber‑Gribov color‑fluctuation model to determine the number of nucleon‑nucleon sub‑collisions, followed by multi‑parton interactions (MPI), initial‑ and final‑state radiation, Lund string fragmentation, and optional color reconnection. The generator relies on collinear factorization for the perturbative part, supplemented by a Gaussian primordial kₜ to emulate non‑perturbative transverse momentum. In contrast, the kₜ‑factorization calculation uses unintegrated gluon distributions (UGDs) obtained from solutions of the running‑coupling Balitsky‑Kovchegov (rcBK) equation with AAMQS initial conditions. A log‑normal distribution of the saturation scale Qₛ is introduced to model event‑by‑event fluctuations, and the KKP fragmentation function converts produced gluons into charged hadrons.

The simulated multiplicity spectra reveal several key findings. First, the α‑cluster geometry systematically yields higher average multiplicities (≈5–8 % increase) and a markedly enhanced high‑multiplicity tail, especially for |η| > 2 and at the highest √s. This effect is attributed to the presence of localized dense regions that increase the probability of multiple parton scatterings and amplify saturation effects. Second, the two theoretical approaches produce distinct shapes: Pythia’s distribution is smoother, reflecting the dominance of soft MPI and color reconnection, whereas the kₜ‑factorization results exhibit a pronounced tail driven by fluctuations of Qₛ and the intrinsic non‑linear dynamics of the CGC.

KNO scaling is examined by plotting ψ(z)=⟨N⟩P(N) versus the scaled variable z = N/⟨N⟩. Both models respect KNO scaling in the intermediate region (0.5 < z < 2), but deviate for large z (z > 3), with the α‑cluster case showing the strongest violation. This indicates that the geometric clustering and saturation dynamics break the scale‑invariance assumption underlying KNO scaling, particularly for rare high‑multiplicity events.

To quantify the contributions of soft and semi‑hard processes, the multiplicity distributions are fitted with a double Negative Binomial Distribution (double NBD): P(N)=α·NB(k₁,μ₁)+(1‑α)·NB(k₂,μ₂). The fit parameters reveal that the α‑cluster configuration significantly enhances the semi‑hard component: the second NBD’s shape parameter k₂ becomes smaller (broader tail) and its mean μ₂ increases relative to the soft component (μ₂/μ₁ ≈ 1.3–1.5). In the Woods‑Saxon case, k₂ remains larger and μ₂/μ₁ stays near 1.1, indicating a weaker semi‑hard contribution.

Overall, the study demonstrates that (i) the initial nuclear geometry—whether smooth Woods‑Saxon or clustered α‑structure—has a measurable impact on charged‑particle multiplicities, especially at large pseudorapidity and in the high‑multiplicity tail; (ii) Pythia and CGC‑based kₜ‑factorization provide complementary but distinct pictures of particle production, highlighting the role of soft MPI versus saturation‑driven gluon dynamics; (iii) deviations from KNO scaling and the double‑NBD analysis both point to an increased relevance of semi‑hard processes when the nucleus is clustered; and (iv) forthcoming LHC Run 3 p‑O data will be crucial for testing these predictions and for refining models of the initial state in small‑system heavy‑ion collisions. The authors suggest that observables sensitive to the high‑multiplicity tail and forward rapidities constitute promising probes for discriminating between nuclear geometry scenarios and for constraining the underlying QCD dynamics in proton‑oxygen interactions.