1. IOPP, Huazhong Normal University, Wuhan, China
Anisotropic flow & multiplicity
in relativistic heavy ion collisions
Wang Meijuan & Wu Yuanfang
IOPP, Huazhong Normal University, Wuhan, China
Motivation
Anisotropic flow and multiplicity at fixed impact parameter in AMPT
3. Initial eccentricity and multiplicity at fixed b in AMPT
4. Summary and Discussions
ATHIC’08

2. coordinate-space-anisotropy  momentum-space-anisotropy
1. Motivation:
★ Anisotropic flow
coordinate-space-anisotropy  momentum-space-anisotropy py px y x
Z : beam direction
out-of-plane direction
in-plane direction
Anisotropic flow parameter v2:
In non-central nucleus-nucleus collisions, the initial overlap zone is an almond shape.
This eccentricity makes the pressure gradient larger in in-plane direction in coordinate space.
It drive the overlap zone expand along in-plane direction. So the final transverse-momentum distribution is
in-plane like.
In fact , what we observed up to now is only the second coefficient of Fourier expansion of azimuthal distributions.
It describes the anisotropic distribution of transverse momentum.
Such a dis. is supposed to be driven by
However, this global measure itself is not able to tell if this pressure gradient is the only driver of anisotropic dis.,
since it does not contain the information of intrinsic interactions of the formed matter.
So v-2 is insufficient in judging whether the formed matter behaves like hydrodynamic flow or not.
It is supposed to be mainly due to initial eccentricity.
ATHIC’08

3. 1. Motivation ★ Anisotropic flow, impact parameter & multiplity
For Au + Au collisions at 200 GeV from AMPT with string melting
In mid-central collisions, elliptic flow has its maximum value, where the spatial anisotropy of the overlap region is the largest.
Does the multiplicity dependence of v2 completely own to
initial geometrical eccentricity, or impact parameter?
ATHIC’08

4. ★ Multiplity dependence of v2 at fixed impact parameter
2. Anisotropic flow and multiplicity at fixed impact parameter in AMPT
★ Multiplity dependence of v2 at fixed impact parameter
For Au + Au collisions at 200 GeV from AMPT with string melting
☞ v2 change with multiplicity
monotonically at fixed b.
☞ v2 depends differently on
Nch at different b.
☞ If Npart is further fixed，the v2 still increases with Nch at both
b=8fm and b=12fm. This may be understandable as the large
Nch comes from more binary coll. and lead to the stronger anisotropy.
We use AMPT with string melting as an example, where the initial geometry is described by
commonly used Glauber model.
ATHIC’08

5. ★ Npart dependence of v2 at fixed impact parameter
2. Anisotropic flow and multiplicity at fixed impact parameter in AMPT
★ Npart dependence of v2 at fixed impact parameter
Anisotropic flow depends on the number of participant
at fixed impact parameter, but differently for different
impact parameters. This is the same as Nch dependency.
ATHIC’08

6. 3. The initial eccentricity and multiplicity at fixed b
M. L. Miller, K. Reygers, S. J. Sanders, P. Steinberg, PRC77：014906(2007).
ATHIC’08

7. 3. The initial eccentricity and multiplicity at fixed b
★ Eccentricity, Npart and multiplicity at fixed b:
☞Initial eccentricity always
decrease with Nch at diff. b
☞Initial eccentricity almost
cont. at diff. b and Npart.
decrease with Npart at diff. b
The Nch dependence of initial eccentricity is diff. from that of elliptic flow.
Anisotropic flow is not completely determined by the initial eccentricity of overlap zone !
ATHIC’08

8. Thanks/谢 谢 ！ 4. Summary and discussions
In AMPT with string melting, we show that,
● At fixed impact parameter, the anisotropic flow still changes monotonically with Nch.
● Initial eccentricity always decrease with multiplicity, in contrary to the multiplicity dependence of anisotropic flow.
● The multiplicity dependence of v2 does not completely own to initial eccentricity. Late expansion and interactions contribute to anisotropic flow too.
● This complicated situation should be taken into account in the further investigation of anisotropic flow.
Thanks/谢 谢 ！
ATHIC’08