Study of Azimuthal Anisotropy of High-p T Charged Particles in Au + Au Collisions at √ s NN = 200 GeV with RHIC-PHENIX †

We study the path length dependence of energy-loss in the Quark Gluon Plasma (QGP) by measuring the azimuthal anisotropy coefficient and transverse momentum (pT) spectra for charged hadrons in Au + Au at √ sNN = 200 GeV at the RHIC-PHENIX experiment. To estimate the strength of 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 for each centrality. The difference of the path length increases along with the centrality and the tendency is the same with the ∆pT results.


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In high energy heavy ion collisions, hard scattered partons can loose their energy because of the 12 interaction with QGP. From the previous results of the nuclear modification factor R AA , it is suggested 13 that the energy-loss plays an important role for the suppression of the yields in QGP relative to nucleon 14 scattering. The previous study in PHENIX by using Au + Au collisions and proton + proton (p + p) 15 collsions [1] has been focused on understanding the strength of energy loss. It compares the strength 16 of the energy loss as a function of transverse momentum (p T ) in Au + Au collision from the central 17 collision to the peripheral to that in p + p. The study indicates that the amount of the energy loss at all 18 centralities tends to be independent of the p T . In this research, we intend to clarify the path-length 19 dependence of the QGP energy-loss. The hard scattered partons have different QGP path-lengths 20 depending on the azimuthal angle of the particle emission. The yield difference at the different 21 azimuthal angle for high-p T particles in the momentum space can be seen as a result of the different 22 amount of energy-loss in the QGP since the original emission angle should be isotropic, azimuthally.

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In this analysis, we use the azimuthal anisotropy coefficient (v 2 ) to estimate the azimuthal-angle 24 dependence of the particle yield. The analysis using v 2 is unique and has advantages that cancel the 25 systematic errors comparing to the previous method [1], since this method uses only the Au + Au we can calculate it more accurately.

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Submitted to Proceedings, pages 1 -4 www.mdpi.com/journal/proceedings 2. Analysis methods 29 We assume that the azimuthal distribution follows the equation (1) since we consider only v 2 component in this analysis.
We use two previous results, inclusive p T spectra and the azimuthal anisotropy v 2 for charged hadrons, 30 to obtain the "in-plane yield" and the "out-of-plane yield". The "in-plane" means the plane parallel to 31 the reaction plane direction while the "out-of-plane" is the one perpendicular to that. For this study,   2 shows the differential yield as a function of the p T 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 blue points show the particle yields in the in-plane and the out-of-plane, respectively. We fit these yields by a function, f(p T ), given in Eq.
We determine the values of these parameters, separately, by fitting the inclusive in-plane and 43 out-of-plane yield. By using the fitting results, one can obtain the values of p T s, p T,in and p T,out , 44 that give the same in-plane and out-of-plane yields, respectively ( f (p T,in ) = f (p T,out )). We define the 45 difference ∆p T = p T,in -p T,out as the estimator of the energy-loss within QGP for given p T .

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The obtained values of ∆p T are shown in Fig.4 as a function of p T for the various centrality regions 48 from 0 to 50% in 10% steps. In each figure, the vertical axis is ∆p T and the horizontal is the in-plane p T .

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For low p T the ∆p T increases as p T increases. On the other hand, at high p T , ∆p T is almost constant, i.e.

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∆p T does not depend on its own p T . The results indicate that the mechanisms causing the ∆p T seem to 51 be different between low p T and high p T . This is consistent with the previous pictures that the yield 52 difference between in and out of plane at low p T is due to the elliptic flow [5] and that at high p T is 53 due to the parton energy loss described in the introduction. The results also indicate that although the 54 shapes are similar for each centrality, for 0 -30% centrality, it tends to increase ∆p T as centrality goes 55 up, and for 30 -50% centrality it increases more gently.

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In order to study the relation between the ∆p T and the parton path length within the QGP, we

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We obtain the in-plane and out-of-plane yields from the inclusive p T spectra and the v 2 67 measurement using our previous results. From these yields, we estimate the transverse momentum 68 loss, ∆p T , as a function of p T (in-plane) for the centrality 0 to 50 %. The ∆p T seems to be independent 69 of its p T at high p T . The dL increases along with the centrality and the tendency is the same as for the 70 ∆p T results. 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.