Unshadowing the constituent quark number scaling of harmonic flow in heavy-ion collisions

Abstract

Constituent quark number scaling of elliptic flow has been proposed as one key observable to identify the phase transition or the absence of the Quark-Gluon Plasma (QGP) in heavy-ion collisions. At the fixed target program at RHIC the STAR collaboration has recently reported that NCQ scaling breaks when decreasing the collision energy from $\sqrt{s_\mathrm{NN}} = 4.5$ to $3.0$ GeV. However, the generation of elliptic flow is dominated by a highly intricate interplay of spectator shadowing, squeeze-out and geometry dependent hadron emission governed by their cross sections. Therefore in this article we will disentangle the shadowing contribution from the harmonic flow signal of the particle emitting source, effectively ``unshadowing'' the source. We introduce Fourier coefficients that quantify the azimuthal absorption rate of hadrons decoupling from the system. We benchmark the derived results using a toy model based on a ballistic Glauber description of the penetrating nuclei and calculate how shadowing qualitatively alters the constituent quark number scaling of the hadron emitting source. The results are thus relevant for interpreting recent STAR measurements as well as the upcoming measurements by CBM at FAIR.

Figures (1)

• Figure 1: [Color online] The measureable elliptic flow $\mathcal{V}_2$ (first column), scaled elliptic flow $\mathcal{V}_2/N_q$ (second column), second order shadowing coefficient $p_2^h$ (third column) and scaled unshadowed elliptic flow $(\mathcal{V}_2 - p_2^h)/N_q$ (fourth column) of $\pi$ (dashed red line), $K$ (dashed blue line), $\overline{K}$ (dashed orange line), $\Phi$ (dashed pink line), $p$ (dotted red line) and $\Lambda$ (dotted blue line) in comparison to the idealized results without shadowing of partons (solid black line), mesons (dashed black line) and baryons (dotted black line) in peripheral Au+Au collisions ($b=7$ fm) at $\sqrt{s_\mathrm{NN}}=3.0$ GeV (upper row) and $\sqrt{s_\mathrm{NN}}=7.7$ GeV (lower row). The results were calculated assuming that hadrons are formed by quark coalescence and emitted isotropically at $t_\mathrm{overlap}$ at the origin at midrapidity $y=0$. The shadowing coefficients were calculated using the presented toy model consisting of a ballistic Glauber density profile and constant effective absorption cross sections for the hadrons.