Abstract
Minijets provide useful information on parton interactions in the low transverse-momentum (low-$p_T$) region. Because minijets produce clusters, we study the clustering properties of produced particles in high-energy $pp$ collisions as a first step to identify minijets. We develop an algorithm to find clusters by using the k-means clustering method, in conjunction with a k-number (cluster number) selection principle in the space of pseudorapidity and azimuthal angles. We test the clustering algorithm using events generated by PYTHIA 8.1, for $pp$ collision at $\sqrt{s}=200$ GeV. We find that clustering of low-$p_T$ hadrons occurs in high multiplicity events. However similar clustering properties are also present for particles produced randomly in a finite pseudorapidity and azimuthal angle space. To distinguish the dynamics from random generations of events, it is necessary to examine the correlation between particles and between clusters. We find that the correlations between clusters may provide a useful tool to distinguish the underlying dynamics of the reaction mechanism.
Highlights
The parton-parton hard scattering is an important process in high-energy nucleon-nucleon collisions
As a first attempt to identify minijets, we develop an algorithm to search for clusters using the k-means clustering method, supplemented with a k-number selection principle
The method adopts a scheme of random initialization of the initial centers, minimizing the potential function ΦðKÞ for a fixed K, and looking for the K number of clusters that leaves the fewest number of particles Ω outside the cluster circles
Summary
The mechanism of relativistic parton-parton hard scattering is an important basic perturbative QCD particle production process in high-energy nucleon-nucleon collisions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Because of the composite nature of a nucleon, multiple hard scattering between partons of the projectile and target nucleons will lead to the production of jets and dijets whose subsequent fragmentation gives rise to the production of particle clusters. We would like to develop tools to study multiple hardscattering processes for the production of multiple minijets and mini-dijets in the low-pT domain in pp collisions at high energies. We include the results of the azimuthal angular correlations and pseudorapidity correlations in the Appendix
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