Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV

TL;DR

The paper presents a comprehensive CMS measurement of charged-particle elliptic flow $v_2$ in PbPb collisions at $\sqrt{s_{NN}}=2.76$ TeV over $0.3<p_T<20$ GeV/$c$ and $|\eta|<2.4$ across 12 centrality classes, using event-plane, cumulants, and Lee–Yang zeros methods. It demonstrates consistent $v_2$ behavior across methods, shows $v_2(p_T)$ rising to ~3 GeV/$c$ and then falling, and reveals that when $v_2$ is scaled by the participant eccentricity $\epsilon_{part}$, or its cumulant moments, it follows a universal scaling with transverse particle density across collision systems and energies. The results constrain initial-state fluctuations and transport properties of the sQGP, supporting a hydrodynamic interpretation with viscosity effects and providing cross-energy continuity with RHIC data. They also quantify pseudorapidity dependence and spectral evolution, offering key inputs for refining models of heavy-ion dynamics and the QCD medium’s evolution.

Abstract

The anisotropy of the azimuthal distributions of charged particles produced in PbPb collisions with a nucleon-nucleon center-of-mass energy of 2.76 TeV is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee--Yang zeros. The anisotropy is presented as a function of transverse momentum (pt), pseudorapidity (eta) over a broad kinematic range: 0.3 < pt < 20 GeV, abs(eta) < 2.4, and in 12 classes of collision centrality from 0 to 80%. The results are compared to those obtained at lower center-of-mass energies, and various scaling behaviors are examined. When scaled by the geometric eccentricity of the collision zone, the elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies.

Figures (25)

• Figure 1: A schematic diagram of a noncentral nucleus-nucleus collision viewed in the plane orthogonal to the beam. The azimuthal angle $\varphi$, the impact parameter vector b, and the reaction-plane angle $\Psi_{\textrm{R}}$ are shown. The event-plane angle $\Psi$, with respect to which the flow is measured, fluctuates around the reaction-plane angle.
• Figure 2: (Color online) A schematic view of a PbPb collision with an impact parameter $b = 6$$\text{\,fm}$ as obtained from the Glauber model. The nucleons that participate in inelastic interactions are marked with filled circles. The x and y coordinates represent the laboratory frame, while x' and y' represent the frame that is aligned with the axes of the ellipse in the participant zone. The participant eccentricity $\epsilon_{\text{part}}$ and the standard deviations of the participant spatial distribution $\sigma_{y'}$ and $\sigma_{x'}$ from which the transverse overlap area of the two nuclei is calculated are also shown. The angle $\Psi_{\textrm{R}}$ denotes the orientation of the reaction plane.
• Figure 3: (Color online) Efficiency (top), fake rate (middle), and momentum resolution (bottom) of charged tracks obtained from hydjet simulated events in four pseudorapidity regions: $|\eta| < 0.8$, $0.8 < |\eta| < 1.6$, $1.6 < |\eta| < 2.0$, and $2.0 < |\eta| < 2.4$ displayed from left to right, and for the five centrality classes given in the legend.
• Figure 4: (Color online) Event-plane resolution correction factors as a function of centrality for the two event-planes (HF- and HF+) used in determining the elliptic anisotropy parameter $v_2$. The corrections determined with the three-subevent method used in the analysis are shown as open squares and star symbols. The results from a two-subevent method used in evaluating the systematic uncertainties are shown as filled circles, though they overlap the other points in all but the most peripheral bin.
• Figure 5: (Color online) An example of the modulus of the second harmonic Lee--Yang zero generating function $G^{\theta}(ir)$ as a function of the imaginary axis coordinate $r$ for $\theta$ = 0. Both the sum and product generating functions are shown, calculated from events with centrality $15$--$20\%$, $|\eta| < 0.8$, and $0.3 < p_{\mathrm{T}}\xspace < 12$${\,\text{Ge\spaceV\space/\space}c}$. An enlargement of $|G^{\theta}(ir)|$ around its first minimum is shown in the inset.