Disentanglement of hard and soft QCD processes using two-particle correlation functions

Transverse spherocity (S 0) has evolved as a powerful method to distinguish between soft and hard contributions in an event in small collision systems. We used the two-particle differential-number correlation functions (R 2) and transverse momentum correlation functions (P 2) of charged particles produced in pp collisions at s=7 TeV with the PYTHIA8 model to explore this phenomena. The Δφ projections of these correlation functions in different multiplicity and S 0 classes are discussed. We find that these correlation functions show different shapes and sizes in both near- and away-side with multiplicity and S 0 classes. We observe a strong correlation in the near- and away-side of these correlation functions for jetty-like (hard QCD processes), which become weaker for isotropic (soft QCD processes) in spherocity classes as compared to multiplicity classes. Finally, it is observed that S 0 should be a good observable as compared to multiplicity to disentangle hard and soft QCD processes in a small collision system.


Introduction
The particle production mechanism is revealed by studying the correlation functions of the charged particles at relativistic energies at RHIC and LHC [1,2].The differential number correlator, R 2 , and transverse momentum correlator, P 2 , are sensitive to the particle production mechanisms and transverse momentum fluctuations [3], respectively.In order to distinguish between the contributions of the hard and soft processes in an event, transverse spherocity (S 0 ), an event shape variable, and multiplicity dependent results for R 2 and P 2 for different percentile classes were compared in this study.This helps to understand the sensitivity of these correlators to regions dominated by jets as well as underlying events in pp collisions.In this study, the events are selected with a minimum constraint of 15 charged particles in the p T range 0.15 -10 GeV/c and |η| < 0.8 in pp collisions at √ s = 7 TeV with the PYTHIA8 [7] event generator.

Definitions of observables
We start by defining the two-particle correlation functions that will be used in this study in Sec.2.1, then we go on to Sec. 2.2 to define the transverse spherocity.
2.1.Two-particle correlation functions: R 2 and P 2 The R 2 [4,5] is defined as a ratio between two-particle density (ρ 2 ) and the product of single particle densities (ρ 1 ), then subtracted by unit in ∆η-∆ϕ space as follows Similarly, P 2 [4,5] is defined as the ratio of differential correlator ( ∆p T ∆p T ) to the square of the mean transverse momentum, p T , to make it dimensionless like R 2 , in ∆η-∆ϕ space as follows . ( where ∆p T,i = p T,i − p T and p T is the inclusive mean transverse momentum.Due to angular and transverse momentum ordering in the production of particles from jets and hadronic resonance decays, P 2 is driven by the momentum of the correlated particles, which is important in comparison to R 2 .

Spherocity (S 0 )
Transverse spherocity [6], simply known as spherocity, is used to distinguish between hard and soft QCD processes and is given by where n(n T , 0) is the unit vector which minimizes S 0 .S 0 varied from 0 for jetty-like events, to a maximum of 1 for isotropic events.In order to better comprehend the spherocity observable, the projection of R 2 (∆η, ∆ϕ) and P 2 (∆η, ∆ϕ) correlation functions along ∆ϕ is investigated for ten equal percentile classes in spherocity as well as multiplicity.

Results
The projections of R 2 (∆η, ∆ϕ) and P 2 (∆η, ∆ϕ) correlation functions onto ∆ϕ are shown for different multiplicity classes (left panel) and spherocity classes (right panel), respectively, in Figs.1-2.In comparison to multiplicity classes, the near-and away-side peak of R 2 and P 2 is more pronounced and distinct for spherocity classes.Again, because of the angular ordering of the jet constituents [5], P 2 is narrower than R 2 .

Summary
We presented a study of the two-particle differential-number correlation functions, R 2 , and transverse momentum (p T ) correlation functions, P 2 , of charged particles for different multiplicity and spherocity classes in pp collisions at √ s = 7 TeV using PYTHIA8 Monte Carlo model.In comparison to multiplicity classes, the magnitude of the modulation has a significantly stronger correlation with spherocity classes for both R 2 and P 2 .Additionally, it is noticed that the near-side peak of P 2 is narrower than that of R 2 , which is mostly due to the angular ordering of hadrons produced in jets.