Proceedings

Study of azimuthal anisotropy of √high-pT charged
particles in Au + Au collisions at s N N = 200 GeV
with RHIC-PHENIX†
Risa Nishitani 1 for the PHENIX Collaboration
1Department of Physics, Nara Women’s University, Nara 630-8506, Japan. ; rar_nishitani@cc.nara-wu.ac.jp†Presented at Hot Quarks 2018 - Workshop for young scientists on the physics of ultra relativistic
nucleus-nucleus collisions, Texel, The Netherlands, September 7-14 2018

Version December 25, 2018 submitted to Proceedings
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Abstract: We study the path length dependence of energy-loss in the Quark Gluon Plasma (QGP) bymeasuring the azimuthal anisotropy coefficient and transverse momentum (pT ) spectra for charged√hadrons in Au + Au at s NN = 200 GeV at the RHIC-PHENIX experiment. To estimate the strengthof the energy-loss as a function of pT , we use the ∆pT which is the difference of pT which provide
the same yields at in-plane and out-of-plane directions. The results indicate that there are different
structures between low-pT and high-pT regions. At high-pT , the size of ∆pT increases as the centrality
goes up. We also calculate the difference of the path length of in-plane and out-of-plane directions foreach centrality. The difference of the path length increases along with the centrality and the tendency
is the same with the ∆pT results.
Keywords: Quark Gluon Plasma, Azimuthal anisotropy, energy-loss, high transverse momentum.

1. Introduction
In high energy heavy ion collisions, hard scattered partons can loose their energy because of theinteraction with QGP. From the previous results of the nuclear modification factor R AA , it is suggested
that the energy-loss plays an important role for the suppression of the yields in QGP relative to nucleon
scattering. The previous study in PHENIX by using Au + Au collisions and proton + proton (p + p)
collsions [1] has been focused on understanding the strength of energy loss. It compares the strengthof the energy loss as a function of transverse momentum (pT ) in Au + Au collision from the central
collision to the peripheral to that in p + p. The study indicates that the amount of the energy loss at all
centralities tends to be independent of the pT . In this research, we intend to clarify the path-length
dependence of the QGP energy-loss. The hard scattered partons have different QGP path-lengths
depending on the azimuthal angle of the particle emission. The yield difference at the different
azimuthal angle for high-pT particles in the momentum space can be seen as a result of the different
amount of energy-loss in the QGP since the original emission angle should be isotropic, azimuthally.
In this analysis, we use the azimuthal anisotropy coefficient (v2 ) to estimate the azimuthal-angle
dependence of the particle yield. The analysis using v2 is unique and has advantages that cancel thesystematic errors comparing to the previous method [1], since this method uses only the Au + Au
collision system. The strength of energy loss can be investigated by measuring the v2 at high p T , andwe can calculate it more accurately.

Submitted to Proceedings, pages 1 – 4

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2. Analysis methods
We assume that the azimuthal distribution follows the equation (1) since we consider only v2
component in this analysis.
dN/dφ ∝ 1 + 2v2 cos(2φ)
(1)

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We use two previous results, inclusive pT spectra and the azimuthal anisotropy v2 for charged hadrons,
to obtain the "in-plane yield" and the "out-of-plane yield". The "in-plane" means the plane parallel tothe reaction plane direction while the "out-of-plane" is the one perpendicular to that. For this study,
we use preliminary results of the azimuthal anisotropy v2 measured by the PHENIX experiment in√Au + Au collisions at s NN = 200 GeV in 2014 data shown in Fig.1 [2] [3]. The inclusive pT spectrum√Figure 1. Azimuthal anisotropy coefficient v2 as a function of pT in Au + Au at s NN = 200 GeV (PHENIX preliminary results [3], for different region of the centrality from 0 − 10% to 40 − 50%. The
results are shown by different symbols as explained in the legend.). Bars indicate the statistical errors
and boxes indicate the systematic errors.
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in Au + Au collisions at s NN = 200 GeV shown as black points in Fig.2, is taken from [4]. For thegiven pT range, one can get the azimuthal distribution, Eq.1, illustrated by the black line in the left
panel of Fig.3. Here, we define the in-plane yield (out-of-plane yield) as the yield where the azimuthal
distribution is assumed to be flat and has a constant value of 1+2v2 (1-2v2 ) which is the value at φ = 0(φ = π/2). The integral value of the black line is equal to the that of the yellow flat line indicated by"inclusive". The right panel in Fig.3 shows a cartoon of the inclusive, in-plane and out-of-plane yields
as a function of pT . These three lines can be obtained from the corresponding distributions for a given
pT in the left panel.

Figure 2. Inclusive, in-plane and out-of-plane yields as a function of pT for the centrality 20-30% in the√Au + Au collisions at s NN = 200 GeV. Bars indicate the statistical errors.

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3 of 4Fig.2 shows the differential yield as a function of the pT in the case of centrality 20 to 30% in Au +√Au collisions at s NN = 200 GeV. The black points are the inclusive yield, while the red and the bluepoints show the particle yields in the in-plane and the out-of-plane, respectively. We fit these yields bya function, f(pT ), given in Eq.(2), where P0 , P1 , P2 , P3 , P4 are parameters to be determined by a fit.
f ( pT ) = P0 ( pT /e P1 pT ) + P2 (1.0 + pT /P3 ) P4434445(2)We determine the values of these parameters, separately, by fitting the inclusive in-plane andout-of-plane yield. By using the fitting results, one can obtain the values of pT s, pT,in and pT,out ,that give the same in-plane and out-of-plane yields, respectively ( f ( pT,in ) = f 0 ( pT,out )). We define thedifference ∆pT = pT,in - pT,out as the estimator of the energy-loss within QGP for given pT .

Figure 3. Left: A typical inclusive azimuthal anisotropic distribution. Right: Cartoon of the inclusive,in-plane and out-of-plane yields as a function of pT
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3. Results

65The obtained values of ∆pT are shown in Fig.4 as a function of pT for the various centrality regions
from 0 to 50% in 10% steps. In each figure, the vertical axis is ∆pT and the horizontal is the in-plane pT .
For low pT the ∆pT increases as pT increases. On the other hand, at high pT , ∆pT is almost constant, i.e.
∆pT does not depend on its own pT . The results indicate that the mechanisms causing the ∆pT seem tobe different between low pT and high pT . This is consistent with the previous pictures that the yield
difference between in and out of plane at low pT is due to the elliptic flow [5] and that at high pT is
due to the parton energy loss described in the introduction. The results also indicate that although theshapes are similar for each centrality, for 0 - 30% centrality, it tends to increase ∆p T as centrality goesup, and for 30 - 50% centrality it increases more gently.
In order to study the relation between the ∆pT and the parton path length within the QGP, wecalculate the distance from the center of the collision to the collision surface in-plane direction (Lin )and the out-of-plane direction (Lout ) as the simplest case. We calculate Lin and Lout geometricallyfrom the relationship between the centrality and the impact parameter of gold nuclei, and take thedifference (dL = Lout − Lin ) between them as shown in the left panel of Fig.5. The radius of the gold
nuclei is taken to be 7.27 × 10−15 m . The right panel of Fig.5 shows the calculated dL as a function ofthe centrality from 0 to 50 %. One can clearly see that dL increases with the centrality up to 30 %. Thisbehavior is in line with the result for ∆pT at higher pT , supporting the interpretation based on a path
length dependent energy loss.

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4. Conclusions

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We obtain the in-plane and out-of-plane yields from the inclusive pT spectra and the v2
measurement using our previous results. From these yields, we estimate the transverse momentum
loss, ∆pT , as a function of pT (in-plane) for the centrality 0 to 50 %. The ∆pT seems to be independentof its pT at high pT . The dL increases along with the centrality and the tendency is the same as for the∆pT results.

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Figure 4. ∆pT v.s. pT of in-plane in Au + Au collisions at s NN = 200 GeV for the centrality region
from 0% to 50% by a 10% step. In this proceeding, we are using an arbitrary scale for the vertical axis.
Error bars indicate statistical errors.

Figure 5. Left: Definition of Lin , Lout and dL. Right: The value of the path-length difference dL as a√function of the centrality in Au + Au collisions at s NN = 200 GeV. Error bars indicate the statisticalerrors.
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c 2018 by the authors.
Submitted to Proceedings for possible open access publication
under the terms and conditions of the Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/).