Methods for the Study of Transverse Momentum Differential Correlations

Abstract

We introduce and compare three differential correlation functions for the study of transverse momentum correlation in $p+p$ and $A+A$ collisions. These consist of {\it inclusive}, {\it event-wise} and a differential version of the correlation measure $\tilde{C}$ introduced by Gavin \cite{Gavin} for experimental study of the viscosity per unit entropy of the matter produced in $A+A$ collisions. We study the quantitative difference between the three observables on the basis of PYTHIA simulations of $p+p$ collisions and $A+A$ collisions consisting of an arbitrary superposition of $p+p$ collision events at $\sqrt{s}=$200 GeV. We observe that {\it inclusive} and {\it event-wise} correlation functions are remarkably identical to each other where as the observable $\tilde{C}$ differs from the two. We study the robustness and efficiency dependencies of these observables based on truncated Taylor expansions in efficiency in $p+p$ collisions and on the basis of Monte Carlo simulation using an adhoc detector efficiency parameterization. We find that all the three observables are essentially independent of detector efficiency. We additionally study the scaling of the correlation measures and find all the observables exhibit an approximate $1/N$ dependence of the number of participants ({\it N}) in $A+A$ collisions. Finally, we study the impact of flow-like anisotropy on the {\it inclusive} correlation function and find flow imparts azimuthal modulations similar to those observed with two-particle densities.

19 pages, 8 figures

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Cited by in corpus (23)

• The ALICE experiment: a journey through QCD
• Transverse-momentum fluctuations in relativistic heavy-ion collisions from event-by-event viscous hydrodynamics
• Evolution of the differential transverse momentum correlation function with centrality in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV
• Higher Flow Harmonics in Heavy Ion Collisions from STAR
• Transverse momentum fluctuations in ultrarelativistic Pb+Pb and p+Pb collisions with wounded quarks
• Correlations in the Monte Carlo Glauber model
• Shear viscosity of nucleonic matter
• Two particle differential transverse momentum and number density correlations in p-Pb and Pb-Pb at the LHC
• Longitudinal and azimuthal evolution of two-particle transverse momentum correlations in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Flow dominance and factorization of transverse momentum correlations in Pb-Pb collisions at the LHC
• Differential two-particle number and momentum correlations with the AMPT, UrQMD, and EPOS models in Pb-Pb collisions at $\sqrt{{\text{s}}_{{}_{\mathrm{NN}}}}$= 2.76 TeV
• Pseudorapidity profile of transverse momentum fluctuations in heavy ion collisions
• Extraction of the specific shear viscosity of quark-gluon plasma from two-particle transverse momentum correlations
• Estimation of shear viscosity based on transverse momentum correlations
• Longitudinal dependence of two-particle momentum correlations from NEXSPHERIO model
• A model investigation of the longitudinal broadening of the transverse momentum two-particle correlator
• Simulation studies of ${\mathrm{R}}_2(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ and ${\mathrm{P}}_2(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ correlation functions in pp collisions with the PYTHIA and HERWIG models
• Effect of centrality bin width corrections on two-particle number and transverse momentum differential correlation functions
• Two-particle transverse momentum correlations in pp and p-Pb collisions at energies available at the CERN Large Hadron Collider
• System size and energy dependence of the mean transverse momentum fluctuations at the LHC
• Differential Correlation Measurements with the Identity Method
• Azimuthal dependence of two-particle transverse momentum current correlations
• Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at $\sqrt{\text{s}}$ = 13 TeV