重离子碰撞中的三角性和偶极不对称性
Triangularity and Dipole Asymmetry in Heavy Ion Collisions
摘要：
我们引入了一种累积展开式来参数化相对论重离子碰撞中可能的初始条件。我们证明了累积量展开的收敛性，并且它能系统地再现Glauber型初始条件的结果。在梯度展开的第三阶，累积量表征初始熵分布的三角形性$<r^3 \cos3(ϕ- ψ_{3,3})>$和偶极不对称性$<r^3 \cos(ϕ- ψ_{1,3})>$。我们发现，对于中部-周边碰撞的偶极不对称$ψ_{1,3}$的取向角有一个$20%$优先出平面。这导致一个小的净$v_1$平面外。在外围和中间-中心碰撞中，取向角$ψ_{1,3}$和$ψ_{3,3}$是强相关的。我们研究了理想流体动力学对这些累积量的响应，并确定了无质量理想气体状态方程的相关$v_1/ε_1$和$v_3/ε_3$。$v_1$和$v_3$向核的边缘发展，因此最终的光谱对冻结的粘性动力学更敏感。$v_3$的流体动力学计算相比，阿尔弗和罗兰适合两个粒子的相关函数。最后，我们建议测量$v_1$与偶极子不对称性和$ψ_{1,3}$和$ψ_{3,3}$之间的相关性通过测量两个粒子的相关性相对于参与者平面，$<\cos(ϕ_a - 3ϕ_b + 2Ψ_{PP})>$。该相关函数的流体动力学预测比STAR协作$<\cos(ϕ_a + ϕ_\b - 2Ψ_{PP})>$目前测量的相关性大几倍。
英文摘要：
We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity $<r^3 \cos3(ϕ- ψ_{3,3})>$ and the dipole asymmetry $<r^3 \cos(ϕ- ψ_{1,3})>$ of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry $ψ_{1,3}$ has a $20%$ preference out of plane. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles $ψ_{1,3}$ and $ψ_{3,3}$ are strongly correlated. We study the ideal hydrodynamic response to these cumulants and determine the associated $v_1/ε_1$ and $v_3/ε_3$ for a massless ideal gas equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and Roland fit of two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole asymmetry and the correlations between $ψ_{1,3}$ and $ψ_{3,3}$ by measuring a two particle correlation with respect to the participant plane, $<\cos(ϕ_a - 3ϕ_b + 2Ψ_{PP})>$. The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, $<\cos(ϕ_a + ϕ_\b - 2Ψ_{PP})>$.
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