%%
%% Manuscript for Quark Matter 2012 Proceedings
%% ============================================
%% Author: Eric Appelt
%% Collaboration: CMS
%% Last updated:
%%
%% This is the class option for the final document
\documentclass[final,1p,times]{elsarticle}
%% Use the option review to obtain double line spacing
%\documentclass[preprint,review,12pt]{elsarticle}
%% Useful/needed packages
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{lineno}
%% Your personal definitions go here
\newcommand{\pt}{$p_{\mathrm{T}}$~}
\newcommand{\pT}{$p_{T}$}
\journal{Nuclear Physics A}
\begin{document}
\begin{frontmatter}
% Your Title - please insert
\title{Elliptic azimuthal anisotropy of charged hadrons and neutral pions in PbPb collisions at 2.76 TeV with CMS}
%% Single author (and collaboration) - please insert
\author{Eric Appelt (for the CMS\fnref{col1} Collaboration)}
\fntext[col1] {A list of members of the CMS Collaboration and acknowledgements can be found at the end of this issue.}
\address{Nashville, TN, United States}
%% Multiple authors
%\author[auth2]{Marcus Junius Brutus}
%\address[auth1]{Somewhere, Rome}
%\address[auth2]{Somewhere else, Rome}
\begin{abstract}
The elliptic flow anisotropies of charged particles and neutral pions ($\pi^{0}$s)
have been measured by the CMS collaboration for PbPb collisions at a nucleon-nucleon
center-of-mass energy of 2.76 TeV. The second Fourier components of the anisotropic
azimuthal distribution are obtained using an event-plane technique for $\pi^{0}$s and four
different analysis techniques for charged particles: event plane, two- and four-particle
cumulants, and Lee-Yang Zeros. These techniques have different sensitivities to non-flow
and flow fluctuation effects and their comparison helps disentangle hydrodynamic flow,
initial state fluctuations and non-flow correlations.
%The results are presented as a function
%of \pt, pseudorapidity, and centrality.
A comparison of the CMS measurements of $v_2(p_{\mathrm{T}})$
from $\pi^{0}$ mesons and inclusive charged particles
%reveals a systematic difference in the
%range of $p_T = 2.5 \sim 5$ GeV/c, with the neutral pion anisotropies being weaker than those
%observed for inclusive charged particles. This difference
indicates a particle-species
dependence in the azimuthal anisotropy at the LHC.
%A systematic comparison of
%the LHC results to lower energy observations is also presented.
\end{abstract}
\end{frontmatter} % do not change
%% linenumbers are useful for reviewing process
%\linenumbers
%\section{Introduction}
The azimuthal anisotropy of charged hadrons and identified particles produced in PbPb collisions
are typically characterized by the coefficients ($v_n$) of Fourier harmonics in an
azimuthal distribution ($\phi$) of the charged particle yield,
$dN/d\phi \propto 1 + \sum^{\infty}_{n=1} 2 v_n \cos{(n(\phi - \Psi_{R} ))}$,
where $\Psi_{R}$ is a reference angle determined event-by-event that corresponds
to a ``participant plane'' defined
by the minor axis of the overlap region and the beam direction.
The coefficient $v_2$, or elliptic flow coefficient, is dominant
in non-central events due to the typically lenticular shape of the overlap region
of the colliding nuclei.
The results presented here include detailed measurements of the elliptic flow of
charged particles produced in PbPb collisions at $\sqrt{s_{_{NN}}}$ = 2.76 TeV
in a broad kinematic range of $ | \eta | < 2.4$, and $0.3 3$ GeV/c) are sensitive to the hadronization
mechanism and the parton energy loss in the medium.
The CMS detector is described elsewhere \cite{JINST}. These analyses use the standard CMS minimum bias
trigger and heavy-ion event selection \cite{jetpaper}. Charged particles are reconstructed using a two-iteration
tracking algorithm, with the first iteration employing signals from the silicon strip and pixel detectors, and the
second iteration reconstructing low-\pt charged particles using only the silicon pixel detectors~\cite{HIN-10-002}. For the event plane
method, the event plane is determined from the azimuthal energy distribution in the forward hadronic
calorimeters. Neutral pions are measured by reconstructing their decay photons ( $\pi^0 \to \gamma\gamma $ )
in the barrel electromagnetic calorimeter (ECAL). Photons are reconstructed in 3x3 arrays of ECAL crystals, which
contain on average 93\% of the photon energy~\cite{HIN-11-009}.
%\section{Results}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.76\textwidth]{v2_pt_3cen_4methods.pdf}
\caption{\label{fig:v2pt}
Comparison of the four different methods for measuring $v_2$ as a function of $p_{\mathrm{T}}$ at mid-rapidity ($|\eta| < 0.8$) for three representative centrality classes given in the figures~\cite{HIN-10-002}. The error bars show the statistical uncertainties only.
}
\end{center}
\end{figure}
In Fig.~\ref{fig:v2pt}, the $v_2$ of charged particles as a function of $p_{\mathrm{T}}$ is given at midrapidity ( $|\eta|<0.8 $) for the
event-plane, two-particle cumulant, four-particle cumulant, and Lee--Yang zeros methods, denoted as
$v_2\{\mathrm{EP}\}$, $v_2\{2\}$, $v_2\{4\}$, and $v_2\{\mathrm{LYZ}\}$, respectively~\cite{HIN-10-002}.
Excepting the $v_2\{2\}$ results in peripheral events
which are dominated by non-flow effects at high-$p_{\mathrm{T}}$, the transverse momentum dependence shows
a rise of $v_2$ up to $p_{\mathrm{T}} \approx 3$ GeV/c and then a decrease.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.70\textwidth]{pi0v2CMSChargedHadronComparison.pdf}
\caption{\label{fig:pizero}
$\pi^0$ meson $v_2$ (solid circles)~\cite{HIN-11-009} compared to charged particle $v_2$
(open squares)~\cite{HIN-10-002} for mid-rapidity ($|\eta|<0.8$). Results are presented as
a function of \pt for six centrality intervals (20-30\% to 70-80\%). Green (gray) shaded bands
represent systematic uncertainties associated with $\pi^0$ meson (charged particle)
$v_2$ measurements.
}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.68\textwidth]{v2eps_cen_3methods.pdf}
\caption{\label{fig:eps_scaling}
Left panel: Centrality dependence of the $p_{\mathrm{T}}$-integrated $v_2$ divided by the participant eccentricity, $\varepsilon_{\mathrm{part}}$, measured at mid-rapidity ($|\eta| < 0.8$) for the event-plane, two-particle cumulant, and four-particle cumulant methods~\cite{HIN-10-002}. Right panel: The same measurements as in the left panel, but here the two-particle and four-particle cumulant results are divided by their corresponding moments of the participant eccentricity, $\varepsilon\{2\}$ and $\varepsilon\{4\}$. In both panels the error bars show the sum in quadrature of the statistical and systematic uncertainties in the measurement of $v_2$, and the lines show the systematic uncertainties in the eccentricity determination.
}
\end{center}
\end{figure}
In Fig~\ref{fig:pizero}, the $\pi^0$ meson $v_2$ results using the event-plane method are shown in six centrality classes
from 20-30\% to 70-80\%~\cite{HIN-11-009} and
compared to inclusive charged particle $v_2$ measured using the event-plane method.
The $\pi^0$ meson $v_2$ is systematically lower than that for inclusive charged particles
$v_2$ between $2.5 < p_{\mathrm{T}} < 5.0$ GeV/c for all six collision centrality intervals. The differences observed
between the inclusive charged particle and $\pi^0$ meson results may be due to the
contribution from baryons which would increase the overall $v_2$ of
the inclusive charged particles, compared to that for neutral pions, assuming a baryon-meson
$v_2$ splitting comparable to that seen at RHIC~\cite{PhysRevLett.92.052302,PhysRevLett.98.162301}.
%\section{Discussion}
In the left panel of Fig.~\ref{fig:eps_scaling}, the $v_2$ obtained from the event-plane and cumulant
methods at midrapidity is integrated over the range $0.3 < p_{\mathrm{T}} < 3.0$ GeV/c, scaled by the participant eccentricity,
denoted by $\epsilon$ or $\epsilon_{\mathrm{part}}$,
as determined from a Monte Carlo Glauber-model simulation, and plotted as a function of centrality.
These data show a near-linear decrease in the eccentricity scaled $v_2$ from central to peripheral collisions.
The values of $v_2$ from the cumulant methods were scaled with
their respective cumulant moments of the participant eccentricity, defined as
$\epsilon\{2\}^{2} \equiv \langle \epsilon_\mathrm{part}^{2} \rangle$
and
$\epsilon\{4\}^{4} \equiv 2 \langle \epsilon_\mathrm{part}^{2} \rangle^{2} - \langle \epsilon_\mathrm{part}^{4} \rangle$.
If the hydrodynamic response to the participant eccentricity is linear, i.e. $v_2 \sim \epsilon$, and nonflow
effects are negligible, then the identity
$v_2\{2\} / \epsilon\{2\} = v_2\{4\} / \epsilon\{4\}$ should hold~\cite{PhysRevC.84.024911}. In the right panel
of Fig.~\ref{fig:eps_scaling}, $v_2\{2\} / \epsilon\{2\}$ and $v_2\{4\} / \epsilon\{4\}$ are plotted and agree in
the centrality range of 15-40\%, suggesting that the difference between these methods can be attributed
to their respective sensitivities to event-by-event flow fluctuations. $v_2\{4\} / \epsilon\{4\}$ deviates from
$v_2\{2\} / \epsilon\{2\}$ in the most central events, where $\epsilon\{4\}$ is very small, and in the most
peripheral events, where fluctuations are large. The difference in the most peripheral events cannot be described
by event-by-event fluctuations as predicted by our Glauber model implementation.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.76\textwidth]{v2_etashifted_3cen_PHOBOS.pdf}
\caption{\label{fig:long_scaling}
Measured $v_2(\eta)$ from CMS~\cite{HIN-10-002} (closed symbols) and PHOBOS~\cite{PhysRevC.72.051901} (open symbols) in three centrality intervals. The left (right) half of each plot shows $v_2$ in the rest frame of the beam moving in the positive (negative) direction. The error bars show the statistical uncertainties, and the boxes show the systematic ones.
}
\end{center}
\end{figure}
The PHOBOS experiment at the Relativistic Heavy Ion Collider (RHIC) has observed that the $v_2$ over a large range of collision energies ranging from $\sqrt{s_{_{NN}}} = 19.6$ GeV to 200 GeV exhibited extended longitudinal scaling when viewed from the rest frame of one of the colliding nuclei~\cite{PhysRevLett.94.122303}. As the measured particles are unidentified in both the CMS and
PHOBOS measurements, the pseudorapidity $\eta^{+}$ $(\eta^{-})$ of the particles in the rest frame of the nucleus moving in the
positive (negative) direction is given by $\eta^{\pm} = \eta \pm y_{\textrm{beam}}$ where $\eta$ is the pseudorapidity of the
particles in the laboratory or center-of-mass frame, and $y_{\textrm{beam}} \approx \ln{\sqrt{s_{_{NN}}} [\textrm{GeV}] }$.
In Fig.~\ref{fig:long_scaling}, the left (right) half of each plot shows $v_2$ in the rest frame of the beam moving in the positive
(negative) direction. The CMS results plotted here are obtained from the event-plane method integrated over the range
$0