Ⅱ-4. Hadron Physics

RIKEN Accel. Prog. Rep. 49 (2016)

Measurements of directed, elliptic, and triangular ﬂow in Cu+Au√
collisions at sN N = 200GeV†
H.Nakagomi∗1∗2 for the PHENIX collaboration†∗1∗2and initial conditions.
Figure 1 shows the sizable v1 measured as the function of transverse momentum pT for four multiplicityclasses. The v1 is measured with respect to the Cu
spectator neutrons that do not participate in the collisions. In all multiplicity classes, high pT particles thatcome from the Au nuclei are indicated by negative v1 .
Figures 2,3 illustrate v2 and v3 measured as functions of pT compared to the hydrodynamical calculation. The event-by-event hydrodynamical calculation
with two diﬀerent viscosities reproduce v2 and v3 simultaneously.
0.02

PHENIX Cu+Au 200 GeV(a)h±v1 w.r.t. Cu spect. neutrons (b)

(c)

(d)

v1

0-0.02-0.04
10-20%
0120-30%234pT (GeV/c)50

140-50%30-40%

2
34pT (GeV/c)

501234pT (GeV/c)

5012
34pT (GeV/c)

5Fig. 1. v1 (pT ) for four diﬀerent multiplicity classes
0.2(a)

v20.15(b)

PHENIX Cu+Au 200 GeVBozek(η/s=0.08)
Bozek(η/s=0.16)

0.1

0.05
020-30%0-5%01

23pT (GeV/c)

45 0123p (GeV/c)

45T

Fig. 2. v2 (pT ) for two diﬀerent multiplicity classes compared to hydrodynamical calculation
0.15

PHENIX Cu+Au 200 GeVBozek(η/s=0.08)
Bozek(η/s=0.16)

0.1(b)(a)v3

In relativistic high-energy heavy-ion collisions, a hotand dense nuclear matter called quark-gluon plasma(QGP) is considered to exist. Until now several measurements and theoretical calculations have suggested
the successful formation of QGP and the produced
QGP is a nearly perfect ﬂuid.
The measurements of the azimuthal anisotropies ofparticle emission is a strong tool to investigate theproperty of QGP. In relativistic heavy-ion collisions,the initial spatial anisotropy of the overlap region of
the oﬀ-center nuclear-nuclear collisions is converted toan anisotropy in momentum space through the pressure gradient. Namely, azimuthal anisotropic ﬂow originates from the initial spatial geometry and is considered to result from the hydrodynamic expansion ofQGP. Thus, azimuthal anisotropy provides us with theinitial spatial condition and the bulk property of QGP.
The azimuthal anisotropic ﬂow is expressed as the coeﬃcients of the Fourier expansion series as follows,dN
2vn cos(n(φ − Ψn ))(1)∝1+dφn=1
where vn = �cos(n(φ − Ψn ))�(n=1,2,3,4...) is the magnitude of azimuthal anisotropy. φ is the azimuthal angle of each particle and Ψn called the nth order EventPlane that is the azimuthal direction in which moreparticles are emitted. The ﬁrst order coeﬃcient is themagnitude of directed particle emission called Directedﬂow. In symmetric collision systems, the signal of Directed ﬂow around the collision point is very small dueto the symmetric interaction region. The second order
coeﬃcient is the magnitude of elliptical particle emission called Elliptic ﬂow. So far the measurements ofv2 have been hardly studied in symmetric collision systems and concluded the viscosity η/s of QGP is small.
The third harmonic coeﬃcient is the magnitude of triangular particle emission called Triangular ﬂow. v3
originates from the initial nucleon ﬂuctuation. The
combined even and odd harmonic coeﬃcients provide
more stringent constraint on the initial condition andthe viscosity of QGP than v2 measurement alone.
In 2012, Cu and Au collisions were operated atRHIC. This was the ﬁrst asymmetric heavy-ion collision for controling initial spatial geometry. In Cu+Au
collisions systems, asymmetric initial conditions leadto an asymmetric pressure gradient and particle production for the Cu and Au side. The measurements ofvn in the Cu+Au collisions further constrain viscosity
Condensed from the article in arXiv:1509.07784 (2015)
RIKEN Nishina Center
Graduate School of Pure and Applied Sciences
University of Tsukuba- 104 -

0.05
00-5%
01

2
3p (GeV/c)
T

420-30%5 0

123p (GeV/c)

45TFig. 3. v3 (pT ) for 2 diﬀerent multiplicity classes comparedto 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) P. Bozek, Phys. Lett. B 717, 287 (2012).
4) A. Adare et al., (PHENIX Collaboration), Phys. Rev.
C 92, 034913 (2015).