RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-4. Hadron Physics

Charged hadron elliptic and triangular flow in Cu+Au at√sN N = 200GeV
H.Nakagomi∗1,∗2 for the PHENIX collaboration
Quark-gluon-plasma(QGP) is considered to be a hot
and dense nuclear matter which is a phase of matter in quantum chromodynamics. A QGP was createdby colliding nuclei at the Relativistic Heavy Ion Collider(RHIC) .
One of the strong evidence to prove the formationof QGP is that the low momentum particle production is anisotropic. Azimuthal anisotropy originatesfrom initial spatial geometry. For low momentum particles, anisotropic collective ﬂow is considered to result
from the hydrodynamic expansion of QGP. Further thestrength of azimuthal anisotropic ﬂow has been used todetermine the speciﬁc viscosity over entropy ratio(η/s)
of QGP and the initial spatial condition by comparing it with the theoretical model. Thus measuring theazimuthal anisotropic ﬂow is a good method to investigate the bulk property of QGP and the space time
expansion mechanism.
The produced particle distribution is expressed as aFourier expansion series as follows∑dN∝1+2vn cos(n(ϕ − Ψn ))
(1)
dϕn=1
where vn = ⟨cos(n(ϕ − Ψn ))⟩ n(1,2,3,4,,,) corresponds
to the strength of anisotropic ﬂow, ϕ is the azimuthal
angle of the produced particle, Ψn is the nth order
event plane that is the average of all emitted particles
angles. So far the 2nd order ﬂow harmonic v2 whichis called elliptic ﬂow has been studied in symmetricsystems such as Au+Au, the 3rd order ﬂow harmonicv3 which is called triangular ﬂow was not predicted
to exist because initial geometry was considered to besymmetric. However recently, a large v3 was measured
at RHIC. The v3 is assumed to have originated fromthe initial spatial ﬂuctuation.
In 2012, a Cu+Au collision was performed at RHIC.
In Cu+Au collisions, the initial spatial geometry isasymmetric. The pressure gradient is predicted to be
diﬀerent for the Au and Cu sides. Thus the diﬀerent
expansion at the Au and Cu sides will lead to the asymmetric emission of particles. The vn in the Cu+Au collision could help determine η/s and the initial spatialcondition.
Figure 1 ilustrates the Npart dependence of v2 andv3 for three collision systems. The system size dependence of v2 is clearly seen. The v2 values in Cu+Au
collisions are between those in Au+Au and Cu+Cu
data sets and v2 in all systems increases as Npart decreases, the diﬀerence of v2 values between the diﬀerent∗1∗2

RIKEN Nishina Center
Graduate School of Pure and Applied Sciences
University of Tsukuba

systems reduce with a decreasing Npart . The Npart dependencies of v2 and v3 could be expected from those of
2nd and 3rd order initial spatial anisotropies(ϵ2 and ϵ3 ).
The ϵ2 and ϵ3 are calculated using a Glauber Monte
Carlo simulation. Figure 2 ilustrates comparison between v2 and v3 as a function of pT with event-byevent hydrodynamical calculation with η/s for 20-30% centrality bin. In this hydrodynamical calculation,
Glauber Monte Carlo simulations are employed as theinitial spatial condition and 4π/s = 1 or 4π/s = 2 isused. The hydrodynamical calculation with 4π/s = 1
has better agreement with v2 and v3 at low pT than4π/s = 2, whereas at high pT hydrodynamical calculation with 4π/s = 2 has better agreement with v2 andv3 than 4π/s = 1.

Fig. 1. Comparison of v2 and v3 as a function of Npart for
four centrality bins in Au+Au, Cu+Cu and Cu+Au

Fig. 2. v2 and v3 as a function of pT for 20-30% centralitybin. Comparison of PHENIX experimental data points
and hydrodynamical calculation

References
1) A. Adare et al (PHENIX Collaboration), Phys. Rev.
Lett. 107 252301 (2011)2) M. R. Haque, M. Nasim, B. Mohanty, Phys. Rev. C 84,067901 (2011)3) Bozek Phys. Lett. B717, 287(2012)- 110 -

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