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 2008.10.14 ATHIC’08

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. 2008.10.14 ATHIC’08

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? 2008.10.14 ATHIC’08

★ 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. 2008.10.14 ATHIC’08

★ 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. 2008.10.14 ATHIC’08

3. The initial eccentricity and multiplicity at fixed b M. L. Miller, K. Reygers, S. J. Sanders, P. Steinberg, PRC77：014906(2007). 2008.10.14 ATHIC’08

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 ! 2008.10.14 ATHIC’08

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 ！ 2008.10.14 ATHIC’08