Probing Azimuthal Alignment in Heavy-Ion Collisions: Clusterization Effects

TL;DR

This study tackles the azimuthal alignment observed in cosmic-ray events by testing whether clustering of secondary particles and event-by-event momentum conservation can induce similar alignment patterns in heavy-ion collisions. Using HYDJET++ to simulate Pb+Pb collisions at $\sqrt{s}=5.02$ TeV, the authors implement a clustering procedure for secondary particles on the emulsion plane and analyze the alignment via the parameter $\lambda_N$ and the degree of alignment $P_N$, while also imposing a residual $p_T$ constraint $|\sum \mathbf{p}_T|<\Delta$ to model momentum conservation. They find that clustering alone is insufficient to reproduce the observed alignment, highlighting the importance of angular correlations and the selection procedure; incorporating the transverse-momentum disbalance enhances $P_N$—especially in the $\Delta\in[0,1]$ GeV range and for certain cluster sizes—bringing qualitative agreement with the Pamir data. The results underscore a significant interplay between local geometric clustering and event-by-event momentum conservation in shaping azimuthal correlations, offering a non-dynamical mechanism to explain alignment-like patterns and informing analyses of non-flow effects in heavy-ion collisions. Overall, the work suggests that azimuthal alignment can emerge from kinematic constraints and clustering in high-multiplicity environments, supplementing the standard flow framework and providing a benchmark for interpreting azimuthal correlations in cosmic-ray and collider contexts.

Abstract

The influence of kinematic constraints and event selection on the emergence of the alignment phenomenon observed in cosmic-ray experiments is studied within the HYDJET++ model. It is demonstrated that the high degree of alignment, previously identified for realistic values of the transverse momentum disbalance of the most energetic particles, is also observed at the level of the most energetic clusters. In high-multiplicity events, the clustering procedure plays a crucial role in resolving individual particle groups on the detection plane, allowing a more accurate characterization of alignment patterns. These results highlight the combined effects of cluster formation and momentum conservation in shaping the observed azimuthal correlations.

Figures (8)

• Figure 1: Kinematics and scheme of the analyzed events in the context of Pamir experiment. Region I represents the Earth’s atmosphere, where incoming cosmic-ray protons generate cascades of hadrons and photons whose alignment properties are studied. Region II corresponds to the emulsion film plane. In this region, $p_i$ stands for the momentum of a registered particle (or cluster), $r_i$ denotes its position on the film, $\phi_i$ is the azimuthal angle, and $h$ indicates the height above the emulsion chamber at which the particle was produced.
• Figure 2: (a) Schematic illustration of a non-central collision of two nuclei in the $xyz$–plane; $\phi$ denotes the azimuthal angle of the outgoing secondary particles. (b) Illustration of three clusters in the azimuthal plane used to study the alignment effect. The angles $\phi_1 = 0$, $\phi_2$, and $\phi_3$ correspond to the azimuthal positions of clusters 1, 2, and 3, respectively. The quantities $\varphi_{123}$, $\varphi_{213}$, and $\varphi_{312}$ represent the angles between the vectors connecting the clusters and are used in the alignment calculation (see Eq. \ref{['eq:lambda']}).
• Figure 3: The degree of alignment $P_3, P_4, P_5$ for the three, four, five clusters as a function of the disbalance $\Delta$ at the different values of the resolution parameter $r_{\rm res}=0.5,1,2,5$ mm. Centrality class $c=0-5 \%$.
• Figure 4: The degree of alignment $P_3, P_4, P_5$ for the three, four, five clusters as a function of the disbalance $\Delta$ at the different values of the resolution parameter $r_{\rm res}=0.5,1,2,5$ mm. Centrality class $c=40-75 \%$.
• Figure 5: The degree of alignment $P_3, P_4, P_5$ for the three, four, five clusters as a function of the disbalance $\Delta$ at the different values of the resolution parameter $r_{\rm res}=0.5,1,2,5$ mm. Centrality class $c=0-75 \%$.