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Quadrupole spectra derived from 2.76 TeV Pb-Pb identified-hadron $\bf v_2(p_t)$ data

Thomas A. Trainor

Abstract

$p_t$-differential quantity $v_2(p_t)$ is meant to measure elliptic flow manifested by a dense QCD medium formed in high-energy nucleus-nucleus collisions. Elliptic flow may be referred to more neutrally as a cylindrical quadrupole component of the transverse motion of particle sources within a collision. As defined, $v_2(p_t)$ relies on an implicit assumption that almost all produced particles emerge from a single source. This article describes a detailed study of the algebraic structure of $v_2(p_t)$. A procedure is developed to derive a common monopole boost (radial flow) value and quadrupole $p_t$ spectra for several hadron species. The method is applied to $v_2(p_t)$ data for three hadron species from 2.76 TeV Pb-Pb collisions. According to available $v_2(p_t)$ data the assumption of a single dominant particle source within A-A collisions is unjustified. Combined with a previous study of quadrupole amplitude variation for 200 GeV $p$-$p$ collisions these results demonstrate that quadrupole structure is related to a novel QCD process separate from projectile-nucleon dissociation and jet production. Given quadrupole evolution it is unlikely that a hydrodynamic description is relevant to that process.

Quadrupole spectra derived from 2.76 TeV Pb-Pb identified-hadron $\bf v_2(p_t)$ data

Abstract

-differential quantity is meant to measure elliptic flow manifested by a dense QCD medium formed in high-energy nucleus-nucleus collisions. Elliptic flow may be referred to more neutrally as a cylindrical quadrupole component of the transverse motion of particle sources within a collision. As defined, relies on an implicit assumption that almost all produced particles emerge from a single source. This article describes a detailed study of the algebraic structure of . A procedure is developed to derive a common monopole boost (radial flow) value and quadrupole spectra for several hadron species. The method is applied to data for three hadron species from 2.76 TeV Pb-Pb collisions. According to available data the assumption of a single dominant particle source within A-A collisions is unjustified. Combined with a previous study of quadrupole amplitude variation for 200 GeV - collisions these results demonstrate that quadrupole structure is related to a novel QCD process separate from projectile-nucleon dissociation and jet production. Given quadrupole evolution it is unlikely that a hydrodynamic description is relevant to that process.

Paper Structure

This paper contains 38 sections, 25 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Quadrupole spectrum methods
  3. Single-particle spectrum models
  4. Quadrupole spectrum definition
  5. Inferring $\bf \bar{\rho}_2(y_t,\Delta y_{t0})$ from measured $\bf v_2(y_t)$ data
  6. 200 $\bf GeV$ $\bf Au$-$\bf Au$ quadrupole spectra
  7. NJ quadrupole $\bf v_2(p_t)$ data in two formats
  8. Quadrupole spectra inferred from $\bf v_2(p_t)$ data
  9. 2.76 $\bf TeV$ $\bf Pb$-$\bf Pb$ quadrupole spectra
  10. 2.76 TeV Pb-Pb $\bf v_2(p_t,n_{ch})$ data
  11. Transformation of $\bf v_2(p_t,n_{ch})$ data to common loci
  12. SP spectra vs quadrupole spectra
  13. Mesons, baryons and NCQ Scaling
  14. Centrality and energy trends
  15. $\bf p_t$-integral quadrupole $\bf n_{ch}$/centrality trends
  16. ...and 23 more sections

Figures (18)

  • Figure 1: Left: $v_2(p_t)$ data for three hadron species plotted in a conventional format. The kaon and Lambda data are from 0-80% central 200 GeV Au-Au collisions v2strange. Data representing pions (solid dots) are hadron data for 16-24% 130 GeV Au-Au collisions scaled up by 1.2 v2pions. Newer pion data extending beyond 6 GeV/c (solid triangles) are from Ref. newstarpion. Right: The same data plotted as ratio $v_2(p_t) / p_t(\text{lab})$ on transverse rapidity. The curves labeled R represent a viscous-hydro prediction for identified protons rom. The solid, dashed and dash-dotted curves through data are described in Sec. \ref{['describe']}.
  • Figure 2: Left: Lambda data from Fig. \ref{['x1']} (right, open points) on an expanded $y_t$ scale compared to viscous-hydro theory curve R for protons rom. The open boxes are more-recent Lambda data for 0-10% central Au-Au collisions starnewlambda. The dotted line marks a detector acceptance limit for charged hadrons at $p_t \approx 0.15$ GeV/c. Right: Data from Fig. \ref{['x1']} (right) multiplied by SP spectra in the form $(2/N_{part}) \bar{\rho}_0(y_t)$ derived from hadron spectra in Ref. hardspec. The curves are described in the text.
  • Figure 3: Data from Fig. \ref{['x2']} (right) divided by kinematic factor $p_t' / p_t$ defined in Eq. (\ref{['kine']}) and transformed to $m_t(\text{boost}) - m_i$. Those data, rescaled by the factors indicated in the plot, then coincide on a single locus modeled by distribution $\hat{S}_2(m'_t)$ (solid curve). $\hat{S}_2(m_t)$ spectrum model parameters are quite different from those for SP hadron spectra ppprdhardspec.
  • Figure 4: $v_2(p_t,n_{ch})$ data for four hadron species from seven centrality classes of 2.76 TeV Pb-Pb collisions alicev2ptb. Bars represent statistical and systematic errors combined quadratically.
  • Figure 5: Left: $v_2\{4\}(n_{ch})$$p_t$-integral data for eight centralities of 2.76 TeV Pb-Pb collisions (solid points) alicev2b compared to 62 and 200 GeV $v_2\{\rm 2D\}(n_{ch})$ data trend (open points davidhqv2ptb) and 200 GeV Eq. (\ref{['magic']}) (dotted curve) davidhqnoelliptic. The 200 GeV $p$-$p$ point is described in the text. Right: Quadrupole source boosts $\Delta y_{t0}(n_{ch})$ for seven centralities of 2.76 TeV Pb-Pb collisions (points) inferred from $v_2(p_t,n_{ch})$ data in this study.
  • ...and 13 more figures