Elliptic flow of deuterons in relativistic heavy-ion collisions

Using a dynamical model based on the $\mathit{NN}\to d\pi ,\mathit{NNN}\to \mathit{dN}$, and $\mathit{NN}\pi \to d\pi$ reactions and measured proton and pion transverse momentum spectra and elliptic flows, we study the production of deuterons and their elliptic flow in heavy-ion collisions at RHIC. The results are compared with those from the coalescence model. The deviation of deuteron elliptic flow from the constituent nucleon number scaling expected from the coalescence model and the comparison with the experimental data are discussed in connection to the allowed nucleon phase space in these reactions.

Figure 1

(a) $p_T$ spectrum of protons. The solid line is half of the parameterized nucleon distribution [Eq. (6)]. Experimental data are from Ref. [32] for the minimum-bias proton spectrum (filled square). (b) Nucleon differential elliptic flow $v_2(p_T)$. The solid line is the parameterized one [Eq. (7)] and filled squares are experimental data from Ref. [16].

Figure 2

$p_T$ spectrum (a) and $v_2$ (b) of pions. Solid lines are parametrization of Eqs. (8) and (9). Experimental data are from Refs. [15, 32].

Figure 3

(a) $p_T$ spectrum of deuterons. Experimental data are from Ref. [38] for the minimum-bias collisions (filled circle). (b) Scaled deuteron elliptic flow $v_2$ as a function of $p_T/2$ at $y_d=0$. The dotted line is the nucleon elliptic flow $v_{2,N}$ of Eq. (7). Experimental data are from the PHENIX Collaboration [16] (filled circles) and the STAR Collaboration [17] (filled squares). In both figures, the dashed and solid lines are results from the coalescence model of Eq. (1) and the dynamical model in the present work, respectively.

Figure 4

The allowed regions of ${\mathit{p}}_1$ and ${\mathit{p}}_2$ in $\mathit{NN}\to d\pi$ reaction. The empty space represents the unphysical phase space. Left panels show the phase space in the azimuthal angles ${\varphi }_1$ and ${\varphi }_2$ of the two nucleons and right panels show the phase space in $\left|{\mathit{p}}_{T,1}\right|$ and $\left|{\mathit{p}}_{T,2}\right|$. Upper panels are for $p_{T,d}=0.1$ GeV and lower panels for $p_{T,d}=4.0$ GeV. The deuteron azimuthal angle is fixed at ${\Phi }_d=0$.

Figure 5

Calculated deuteron $p_T$ spectrum (a) and scaled $v_2$ (b) at midrapidity from $\mathit{NN}\to d\pi$ (solid lines), $\mathit{NNN}\to \mathit{dN}$ (dashed lines), and $\mathit{NN}\pi \to d\pi$ (dotted lines) reactions. Experimental data are from Refs. [16, 17].

Figure 6

Diagram for the $\mathit{NN}\to d\pi$ reaction. The blob denotes the $\pi N\to \pi N$ elastic scattering.

Figure 7

Total cross section for the $\mathit{pp}\to d{\pi }^{+}$ reaction. The experimental data are from Refs. [45, 46, 47, 48].

Figure 8

Total cross sections for ${\pi }^{+}p\to {\rho }^{+}p$ (a) and $\mathit{pp}\to d{\rho }^{+}$ (b). Experimental data are from Ref. [49].