ϕ and Ω production in relativistic heavy-ion collisions in a dynamical quark coalescence model

Based on the phase-space information obtained from a multiphase transport model within the string-melting scenario for strange and antistrange quarks, we study the yields and transverse-momentum spectra of $\varphi$ mesons and $\Omega$ (${\Omega }^{-}+{\overline{\Omega }}^{+}$) baryons and their anisotropic flows in Au + Au collisions at RHIC using a dynamical quark coalescence model that includes the effect from quark phase-space distributions inside hadrons. With current quark masses and fixing the $\varphi$ and $\Omega$ radii from fitting measured yields, we first study the ratio of the yield of $\Omega$ baryons to that of $\varphi$ mesons as well as their elliptic and fourth-order flows as functions of their transverse momentum. How the elliptic and fourth-order flows of $\varphi$ mesons and $\Omega$ baryons are related to those of strange and antistrange quarks is then examined. The dependence of these results on $\varphi$ and $\Omega$ radii as well as on the strange quark mass is also studied.

Figure 1

(Color online) Rapidity distributions of strange and antistrange quarks ($s+\overline{s}$) as well as light quarks and antiquarks ($u+\overline{u}+d+\overline{d}$) at freeze-out in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm.

Figure 2

(Color online) Transverse-momentum distributions of midrapidity strange and antistrange quarks ($s+\overline{s}$) as well as light quarks and antiquarks ($u+\overline{u}+d+\overline{d}$) at freeze-out in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm.

Figure 3

(Color online) Number density distribution in the transverse plane for midrapidity strange and antistrange quarks at freeze-out in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm (upper panel) and corresponding contour plot (lower panel).

Figure 4

(Color online) Space-time structure of midrapidity strange and antistrange quarks at freeze-out in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm.

Figure 5

(Color online) Freeze-out rate of midrapidity strange and antistrange quarks as a function of proper time $\tau$ as well as the time t in the nucleus-nucleus center-of-mass system.

Figure 6

(Color online) Time evolution of the energy density in the central cell of partonic matter in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm.

Figure 7

(Color online) Transverse-momentum dependence of elliptic flow $v_2$ (solid squares) and forth-order anisotropic flow $v_4$ (open squares) of midrapidity strange and antistrange quarks ($s+\overline{s}$) at freeze-out in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm. The thick solid line represents $0.85v_2^2$ of strange and antistrange quarks, and open triangles are $v_2$ of midrapidity light up and antiup quarks ($u+\overline{u}$).

Figure 8

(Color online) Transverse-momentum dependence of midrapidity $\varphi$ mesons and $\Omega$ (${\Omega }^{-}+{\overline{\Omega }}^{+}$) baryons (upper panels) and their ratio (lower panels) in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV with $b=0$ fm (left panels) and $b=8$ fm (right panels). Data for $\varphi$ mesons in the $0\%-5$% centrality bin from the STAR Collaboration [38] (solid stars) and in the $0\%\text{−}10$% centrality bin from the PHENIX Collaboration [39] (open stars) as well as preliminary data for $\Omega$ baryons in 0%–$10$% centrality bin from the STAR Collaboration [40] (solid triangles) are shown in the upper left panel; those for the $\Omega /\varphi$ ratio in the $0\%-10$% centrality bin are shown in the lower left panel.

Figure 9

(Color online) Transverse-momentum dependence of the ratio of midrapidity $\varphi$ meson and $\Omega$ baryon yields in central ($b=0$ fm) to that in midperipheral ($b=8$ fm) Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV.

Figure 10

(Color online) Transverse-momentum dependence of anisotropic flows $v_2$ and $v_4$ of midrapidity $\varphi$ mesons (left panel) and $\Omega$ baryons (right panel) produced in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm. Solid and dashed lines in the left panel are, respectively, $1.1v_2^2$ and $1.2v_2^2$ for $\varphi$ mesons; the solid line in the right panel is $0.7v_2^2$ for $\Omega$ baryons.

Figure 11

(Color online) Valence quark number scaled elliptic flow $v_2/n_q$ as a function of scaled transverse momentum $p_T/n_q$ for midrapidity $\varphi$ mesons and $\Omega$ baryons produced in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm with $R_{\varphi }=0.65$ fm (solid squares) and $0.47$ fm (open squares) as well as $R_{\Omega }=1.2$ fm (solid line). Results for midrapidity strange and antistrange quarks ($s+\overline{s}$ ) at freeze-out are shown by solid stars.

Figure 12

(Color online) Hadron size (root-mean-square radius) dependence of rapidity density $\mathit{dN}/\mathit{dy}$ of midrapidity $\varphi$ mesons (solid squares) and $\Omega$ (${\Omega }^{-}+{\overline{\Omega }}^{+}$ ) baryons (open squares) produced in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV with $b=0$ fm (upper panel) and $b=8$ fm (lower panel).

Figure 13

(Color online) Transverse-momentum dependence of the $v_2$ of midrapidity $\varphi$ mesons (left panel) and $\Omega$ baryons (right panel) in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=8$ fm with different values of root-mean-square radii $R_{\varphi }$ and $R_{\Omega }$.

Figure 14

(Color online) Same as Fig. 11 but with $R_{\varphi }=$ $R_{\Omega }=4.5$ fm.

Figure 15

(Color online) Same as Fig. 10 but with $R_{\varphi }=R_{\Omega }=4.5$ fm.

Figure 16

(Color online) Same as Fig. 8 but with $m_s=500$ MeV and $R_{\varphi }=0.5$ or $0.35$ fm and $R_{\Omega }=0.9$ fm.

Figure 17

(Color online) Same as Fig. 10 but with $m_s=500$ MeV and $R_{\varphi }=0.5$ or $0.35$ fm and $R_{\Omega }=0.9$ fm.

Figure 18

(Color online) Same as Fig. 11 but with $m_s=500$ MeV and $R_{\varphi }=0.5$ and $0.35$ fm and $R_{\Omega }=0.9$ fm.