Examining the Necessity to Include Event-By-Event Fluctuations in Experimental Evaluations of Elliptical Flow

Elliptic flow at BNL RHIC is computed event by event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15%–30% for $\eta =0$, 30% for $p_{\perp }=0.5\mathrm{GeV}$). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows.

Figure 1

Comparison between various ways of computing $v_2$ using NeXSPheRIO for Phobos 15%–25% centrality window [9]: solid line is $v_2^b$, obtained using the known impact parameter angle ${\varphi }_b$, dashed (dotted) line is $v_2^{\mathrm{obs}}$ ($v_2^{\mathrm{rec}}$), obtained using the reconstructed impact parameter angle ${\psi }_2$ without (with) reaction plane correction.

Figure 2

Assuming (top) $d^{2}N/d\varphi d\eta =1+2v_2^b\cos [2(\varphi -{\varphi }_b)]+2v_2^{\prime b}\sin [2(\varphi -{\varphi }_b)]$ with ${\varphi }_b=0$: dash-dotted momentum distribution is symmetric with respect to the reaction plane ($v_2^b>0$, $v_2^{\prime b}=0$) and solid is asymmetric ($v_2^b>0$, $v_2^{\prime b}>0$); assuming (bottom) $d^{2}N/d\varphi d\eta =1+2v_2^{\mathrm{obs}}\cos [2(\varphi -{\psi }_2)]+2v_2^{\prime \mathrm{obs}}\sin [2(\varphi -{\psi }_2)]$ with ${\varphi }_b=0$: dashed momentum distribution is symmetric with to the plane inclination ${\psi }_2$ above the impact parameter and containing the beam axis ($v_2^{\mathrm{obs}}>0$, $v_2^{\prime \mathrm{obs}}=0$) and solid is asymmetric ($v_2^{\mathrm{obs}}>0$, $v_2^{\prime \mathrm{obs}}>0$).

Figure 3

Comparison between true elliptic flow $v_2^b$ (solid line) and suggested method to compute reconstructed elliptic flow from data $v_2^{\mathrm{Rec}}$ (dash-dotted) for the three Phobos centrality windows [9]. Squares represent Phobos data (black error bars are $1\sigma$ statistical errors and gray bands, systematic uncertainties at $\sim 90\%$ confidence level).