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Azimuth Quadrupole Spectra derived from 2.76 TeV Pb-Pb PID Differential $v_2(p_t)$ Data

Thomas A. Trainor

Abstract

$v_2(p_t)$ data are intended to estimate the amplitude of an azimuth component of particle spectra interpreted as representing elliptic flow of a dense QCD medium. As defined, $ v_2(p_t)$ is a ratio with a single-particle spectrum appearing in its denominator. Its numerator represents a spectrum Fourier component arising from a boosted particle source. The Cooper-Frye (CF) formalism may be used to describe emission from a boosted source. CF analysis reveals that the $v_2(p_t)$ numerator includes a factor $ p_t$ in the boost frame with major consequences for data interpretation. A unique quadrupole $p_t$ spectrum may be isolated from $v_2(p_t)$ data and compared directly with the single-particle spectrum in the $v_2$ denominator and with hydro theory. A monopole boost (aka radial flow) value may be estimated from $v_2(p_t)$ data. Several novel results emerge via the Cooper-Frye analysis.

Azimuth Quadrupole Spectra derived from 2.76 TeV Pb-Pb PID Differential $v_2(p_t)$ Data

Abstract

data are intended to estimate the amplitude of an azimuth component of particle spectra interpreted as representing elliptic flow of a dense QCD medium. As defined, is a ratio with a single-particle spectrum appearing in its denominator. Its numerator represents a spectrum Fourier component arising from a boosted particle source. The Cooper-Frye (CF) formalism may be used to describe emission from a boosted source. CF analysis reveals that the numerator includes a factor in the boost frame with major consequences for data interpretation. A unique quadrupole spectrum may be isolated from data and compared directly with the single-particle spectrum in the denominator and with hydro theory. A monopole boost (aka radial flow) value may be estimated from data. Several novel results emerge via the Cooper-Frye analysis.

Paper Structure

This paper contains 12 sections, 5 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Elliptic flow, $\bf v_2(p_t)$ and the Cooper-Frye formalism
  3. 200 GeV quadrupole spectra
  4. 2.76 TeV Pb-Pb $\bf v_2(p_t)$ data
  5. Particle source boost variation with event $\bf n_{ch}$
  6. Quadrupole spectra on transverse rapidity $\bf y_{ti}$
  7. Quadrupole spectra on transverse mass $\bf m_{ti}$ in the boost frame
  8. Quadrupole amplitude $\bf V_2^2$ from p-p angular correlations
  9. $\bf V_2^2$ charge-multiplicity and collision-energy dependence
  10. Mesons and baryons -- NCQ scaling
  11. $\bf v_2(p_t)$ vs hydrodynamic theory
  12. Conclusions

Figures (10)

  • Figure 1: (a) $v_2(p_t)$ in conventional format. (b) Revised format with common intercept at $\Delta y_{t0}$. (c) Emphasis on Lambdas. (d) Quadrupole spectra in the lab frame.
  • Figure 2: $v_2(p_t,n_{ch})$ from 2.76 TeV Pb-Pb collisions for (a) pions, (b) charged kaons, (c) protons and (d) Lambdas as published.
  • Figure 3: (a) $v_2(b)$ for 2.76 TeV Pb-Pb collisions (solid dots) and model fits to 2D angular correlations for 62 and 200 GeV Au-Au collisions (open symbols) and 200 GeV $p$-$p$ collisions (solid square). (b) Inferred centrality variation of monopole boost $\Delta y_{t0}$ (points) for 2.76 TeV Pb-Pb collisions. Rescaled $v_2(b)$ data for 2.76 TeV Pb-Pb collisions showing variation of $\Delta y_{t0}$ with centrality for kaons (c) and protons (d).
  • Figure 4: Rescaled 2.76 TeV Pb-Pb $v_2(p_t)$ data in the format of Fig. \ref{['fig1']} (b) shifted to common $\Delta y_{t0}$ for (a) pions, (b) charged kaons, (c) protons and (d) Lambdas.
  • Figure 5: Soft-rescaled SP spectra $X_i(p_t)$ (solid curves) and models defined on $v_2(p_t)$$p_t$ values (solid points) for (a) pions, (b) charged kaons, (c) protons and (d) Lambdas The open symbols in (a) are a Au-Au model for Fig. \ref{['fig1']} (d) for comparison.
  • ...and 5 more figures