Multiplicity and transverse-momentum dependence of two- and four-particle correlations in pPb and PbPb collisions

TL;DR

This study provides a comprehensive, multi-particle analysis of azimuthal correlations in pPb and PbPb collisions, comparing long-range ridge structures and flow harmonics across wide multiplicities and pT ranges. By employing two- and four-particle cumulants, it isolates collective effects from jet-related correlations, revealing a stronger v2 in PbPb yet a remarkably similar v3 between systems at matched multiplicities. The results, including ZYAM-based yields and multi-particle v_n measurements, challenge simple pictures and offer crucial constraints for hydrodynamic and Color Glass Condensate models. The work substantially extends the understanding of collective phenomena in small systems and their connection to heavy-ion collisions.

Abstract

Measurements of two- and four-particle angular correlations for charged particles emitted in pPb collisions are presented over a wide range in pseudorapidity and full azimuth. The data, corresponding to an integrated luminosity of approximately 31 inverse nanobarns, were collected during the 2013 LHC pPb run at a nucleon-nucleon center-of-mass energy of 5.02 TeV by the CMS experiment. The results are compared to 2.76 TeV semi-peripheral PbPb collision data, collected during the 2011 PbPb run, covering a similar range of particle multiplicities. The observed correlations are characterized by the near-side (abs(Delta(phi)~0) associated pair yields and the azimuthal anisotropy Fourier harmonics (v[n]). The second-order (v[2]) and third-order (v[3]) anisotropy harmonics are extracted using the two-particle azimuthal correlation technique. A four-particle correlation method is also applied to obtain the value of v[2] and further explore the multi-particle nature of the correlations. Both associated pair yields and anisotropy harmonics are studied as a function of particle multiplicity and transverse momentum. The associated pair yields, the four-particle v[2], and the v[3] become apparent at about the same multiplicity. A remarkable similarity in the v[3] signal as a function of multiplicity is observed between the pPb and PbPb systems. Predictions based on the color glass condensate and hydrodynamic models are compared to the experimental results.

Figures (11)

• Figure 1: The $c_{2}\{4\}$ values as a function of multiplicity calculated for bin width of 30 (open squares), and first derived using a smaller bin width of 2 (open circles) or 5 (solid circles) and then averaging over the same wider bin of 30, for $\text{pPb}$hijing MC simulations (left) and data (right) at $\sqrt{s_{_{NN}}}$ = 5.02$\,\text{Te\spaceV}$.
• Figure 2: The 2D two-particle correlation functions for (a) 2.76$\,\text{Te\spaceV}$ PbPb and (b) 5.02$\,\text{Te\spaceV}$$\text{pPb}$ collisions for pairs of charged particles with $1<p_\mathrm{T}^{\text{trig}}<3{\,\text{Ge\spaceV\space/\space}c}\xspace$ and $1<p_\mathrm{T}^{\text{assoc}}<3{\,\text{Ge\spaceV\space/\space}c}\xspace$ within the $220 \leq N_\text{trk}^\text{offline}\xspace\ < 260$ multiplicity bin. The sharp near-side peak from jet correlations is truncated to emphasize the structure outside that region.
• Figure 3: The 1D two-particle correlation functions for 2.76$\,\text{Te\spaceV}$ PbPb collisions within the multiplicity range $220 \leq N_\text{trk}^\text{offline}\xspace\ < 260$ (filled squares) and $N_\text{trk}^\text{offline}\xspace\ < 20$ (open squares), for pairs of charged particles with fixed $p_\mathrm{T}^{\text{assoc}}$ 1--2${\,\text{Ge\spaceV\space/\space}c}$ in five $p_\mathrm{T}^{\text{trig}}$ ranges, in the long-range region ($|\Delta\eta|>2$, top) and in the short-range region ($|\Delta\eta|<1$, bottom). The curves on the top panels correspond to the Fourier fits from Eq. (\ref{['eq:Vn']}) including the first three terms.
• Figure 4: The 1D two-particle correlation functions for 5.02$\,\text{Te\spaceV}$$\text{pPb}$ collisions under the same conditions as in Fig. \ref{['fig:corr1D_PbPb_N220260_paper']}.
• Figure 5: Associated event-normalized yield for the near-side correlation function integrated over the region $\lvert \Delta\phi \rvert<1.2$, averaged over the (a) long-range ($|\Delta\eta|>2$) region and (b) short-range ($|\Delta\eta|<1$) region, from which the event-normalized yield of the long-range region is subtracted. The results are shown as a function of $p_\mathrm{T}^{\text{trig}}$ at $1<p_\mathrm{T}^{\text{assoc}}<2$${\,\text{Ge\spaceV\space/\space}c}$ for events with $220 \leq N_\text{trk}^\text{offline}\xspace\ < 260$ for 5.02$\,\text{Te\spaceV}$$\text{pPb}$ collisions (filled circles) and 2.76$\,\text{Te\spaceV}$ PbPb collisions (filled squares). The error bars correspond to statistical uncertainties, while the shaded areas denote the systematic uncertainties.