Title: Azimuthally sensitive $\pi^{\pm}$-$\pi^{\pm}$ femtoscopy in ultra-central U+U and Au+Au collsions at RHIC
PA's: John Campbell and Mike Lisa
Target Journal: PRC
Abstract: We present azimuthally sensitive $\pi^{\pm}$-$\pi^{\pm}$ interferometry analyses of ultra-central U+U collisions at $ \sqrt{s_{NN}} $ = 193 GeV and Au+Au collisions at $ \sqrt{s_{NN}} $ = 200 GeV at the Relativistic Heavy-Ion Collider (RHIC). These measurements provide information on the three dimensional pion source distribution at freezeout, and are studied as functions of multiplicity and the reduced flow parameter $ q_{2} $. Oscillations of the extracted Hanbury-Brown--Twiss (HBT) radii relative to the reaction plane are sensitive to eccentricities in the emitting source, and can indicate whether initial state spatial anisotropies due to the prolate shape of the Uranium nucleus survive the hydrodynamic expansion of the fireball.

Figures

Figure 1: Multiplicity distributions for ultra-central U+U (blue) and Au+Au (red) collisions for the 1% most central ZDC selection. Here we count the number of charged tracks detected in the TPC in the rapidity range | $ \eta $ | < 0.5. Multiplicity has been corrected for detector efficiency and beam luminosity.

Figure 2: Distribution of the reduced flow parameter $ q_{2} $ for ultra-central U+U (blue) and Au+Au (red) collisions for the 1% most central ZDC selection. The two distributions are nearly identical.

Figure 3: Event-plane resolution for 0.5% most central U+U (blue) and Au+Au (red) collisions as a function of scaled multiplicity and $ q_{2} $.

Figure 4: One dimensional projections of the three dimensional correlation function in the out, side, and long directions. Shown here are the projections for the 0.5% most central U+U collisions in the lowest multiplicity bin, for pion pairs emitted at | $ \phi $ | < 22.5 degrees. The data are shown in blue, with the fit to the data shown in red. Projections are made over the range | $ q_{other} $ | < 0.01 GeV.

Figure 5: Oscillations of the HBT radii for U+U (blue) and Au+Au (red) collisions. The point at 0 degrees has been mirrored as an open symbol at 180 degrees for clarity. Dashed lines fits of the form $ A + B cos(2\phi) $ for $R^2_{out}$, $R^2_{side}$, and $R^2_{long}$; and of the form $A + Bsin(2\phi)$ of $R^2_{out-side}$.

Table 1: Values for various HBT parameters for U+U and Au+Au collisions. Statistical uncertainties are listed first, followed by systematic uncertainties.

Table 2: The same as in TABLE 1, but here we show the difference between the two colliding systems. The value for the Au+Au system is subtracted from that of the U+U system.


Figure 6: Average radii and scaled oscillation amplitudes for U+U (blue) and Au+Au (red) collisions as a function of scaled multiplicity. Shaded bands indicate systematic errors.

Figure 7: Average radii and scaled oscillations amplitudes for U+U (blue) and Au+Au (red) collisions as a function of the reduced flow parameter $ q_{2} $. Shaded bands indicate systematic errors.

Conclusions: We have presented measurements of two-particle HBT correlations for ultra-central collisions in two heavy-ion systems: U+U and Au+Au. The average homogeneity lengths for U+U pion sources are systematically larger, owing both to the greater size of the uranium nucleus and the longer lifetime over which the fireball in U+U collisions evolves and expands. The eccentricity of the pion emitting source at freezeout $ \epsilon_{f} $--measured through the scaled oscillation amplitude $ 2 R^{2}_{s,2}/R^{2}_{s,0} $--is greater for U+U than Au+Au, which we attribute to spatial anisotropies present in the initial state of body-body collisions. Additionally, ultra-central Au+Au collisions exhibit a \textit{negative} eccentricity at freezeout, which could indicate an initially round system that evolves to be extended in the direction of the reaction plane. No significant dependence of $\epsilon_{f}$ on either the scaled multiplicity or reduced flow parameter $ q_{2} $ is seen.