Speaker
li Yan
(Stony Brook University)
Description
We introduce a cummulant expansion to parameterize possible initial conditions
in heavy ion collisions. We show that the cummulant expansion converges and can
systematically reporduce the results of the Glauber type initial conditions.
At third order in the gradient expansion, the cummulants are described with the
triangularity $\llangle r^3 \cos3(\phi - \psi_{1,3} ) \rrangle$, and a dipole
assymetry, $\llangle r^3 \cos(\phi- \psi_{1,3}) \rrangle$. We show that the
orientation angle of the dipole assymetry $\psi_{1,3}$
has a $20\%$ assymetry out of plane for mid-central collisons.
This leads to a small net $v_1$ out of plane.
In peripheral and mid-central collisions the
orientation angles $\psi_{1,3}$ and $\psi_{3,3}$ are strongly correlated, but this correlation disappears towards central collisions.
We study the ideal
hydrodynamic response to these cummulants and determine the associated $v_1/\epsilon_1$
and $v_3/\epsilon_3$ for a massless ideal gas. The space time development of $v_1$ and
$v_3$ is clarified with figures. These figures show that $v_1$ 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 $v_3$ is provisionally compared to Alver and Roland fit of STAR inclusive two particle correlation functions. Finally, we propose to
measure the $v_1$ associated with the dipole assymetry by measuring $\llangle \cos(\phi - 3\Psi_{R3} + 2\Psi_{R2}) \rrangle $ where $\Psi_{R3}$
is an experimental estimate for the triangular event plane while $\Psi_{R2}$
is the usual quadrupole event plane plane estimate.
This experimental measurement would provide convincing evidence for the
strong correlation between $\psi_{1,3}$ and $\psi_{3,3}$, and by association
the hydrodynamic interpretation of two particle correlations at RHIC.
Author
li Yan
(Stony Brook University)
