Initial fluctuation effect on
harmonic flows in high-energy
heavy-ion collisions
Yu-Gang Ma
Li-Xin Han
Guo-Liang Ma
Outline
• Introduction
• Initial fluctuation effect on vn @
RHIC
• Initial fluctuation effect on vn @
LHC
• Summary
2
Initial fluctuation
Cu+Cu@200 or 62GeV
Au+Au@200 or 62GeV
• Au+Au
•Cu+Cu
PHOBOS Collaboration
PRL 98, 242302 (2007)
3
even and odd harmonic flow
B Alver and G Roland, Phys. Rev. C 81, 054905 (2010)
ψR
ψ3
ψ2
4
harmonic flow arises due to
initial fluctuation
5
PHENIX (arXiv: 1105.3928)
Why vn matters
The Power Spectrum extracted
from the Cosmic Microwave
Background Radiation.
v2 and v3 together provide more
information about the system like
initial state, lifetime, viscosity etc.
A.P. Mishra, R. K. Mohapatra, P. S. aumia, A. M.
Srivastava, Phys. Rev. C77: 064902, 2008
P. Sorensen, WWND, arXiv:0808.0503 (2008);
J. Phys. G37: 094011, 2010
P. Sorensen, QM 2011
6
K. Werner, et. al (arXiv: 1104.3269 )
Ratio of vn and εn
Derek Teaney and Li Yan, PRC 83, 064904 (2011)
•
•
•
AuAu 200 GeV from AMPT model
Harmonic flow is converted from initial geometry irregularity via parton cascade .
The conversion efficiency (vn/εn) decreases with the order of harmonic flow.
vn/εn increases with cross section, which is consistent with later freeze out.
7
Vn as a function of pT
3 mb
• vn increases after considering initial fluctuation.
• Mass ordering and hadron typing still present for v3 and v4.
8
NCQ scaling of vn
Roy A. Lacay, et. al (arXiv:1105.3782)
• A NCQ scaling of vn/nqn/2 ∝ KET /nq holds for harmonic
flow (vn, n = 2, 3 and 4) in different centrality bins.
9
Similar v2-scaling in low energy HIC
T.Z. Yan, YGM et al., Phys. Lett. B 638, 50 (2006)
•
25A MeV Kr+Sn by QMD model
•
Number of nucleon number of v2 works for nuclear clusters
10
Similar v4-scaling in low energy HIC
T.Z. Yan, YGM et al., Chin. Phys.16, 2666 (2007)
•
25A MeV Kr+Sn by QMD model
•
Number of nucleon number of v2 works for nuclear clusters
11
Vn vs pT for different centrality bins
at RHIC energy
• It seems to prefer a bigger cross section in higher
transverse momentum range.
• v3 shows a less centrality dependence than v2
12
Vn @ LHC from ALICE
ALICE Collaboration,
PRL 107, 032301 (2011)
•
The red line shows the sum of the
measured anisotropic flow Fourier
coefficients.
•
Those flow coefficients give a
natural description of the observed
dihadron correlation (|∆η| > 1).
13
Vn @ LHC from AMPT model
Pb+Pb 2.76 TeV
• Data seem to prefer a bigger cross section in higher
transverse momentum range.
• v3 shows a less centrality dependence than v2.
• Similar to vn @ RHIC.
14
Vn calculated by ψn in momentum
and coordinate spaces
Au+Au 200 GeV
from AMPT model
n=2
EP from final px-py space:
n=3
n=2
EP from initial x-y space:
n=3
• Vn calculated from final momentum event plane (after correcting event
plane resolution) is larger than that from initial geometry event-plane.
• Non-flow contribution should not be ignored for vn measurement, four
particle cumulant method is preferably required to reduce it.
15
Summary
• The conversion efficiency (vn/εn) decreases with the
order of harmonic flow, but increases with partonic cross
section.
• Event-by-event initial geometry fluctuation increases vn .
• Mass ordering and NCQ scaling of vn/nqn/2 ∝ KET /nq
holds for harmonic flow (vn, n = 2, 3 and 4).
• v2 and v3 calculated from final momentum event plane
are larger than that from initial geometry event plane due
to non-flow contribution.
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