Resonance recombination model and quark distribution functions in the quark-gluon plasma

We investigate the consequences of space-momentum correlations in quark phase-space distributions for coalescence processes at the hadronization transition. Thus far it has been proved difficult to reconcile such correlations with the empirically observed constituent quark number scaling (CQNS) at the Relativistic Heavy Ion Collider (RHIC). To address this problem we combine our earlier developed quark recombination model with quark phase-space distributions computed from relativistic Langevin simulations in an expanding quark-gluon plasma (QGP). Hadronization is based on resonance formation within a Boltzmann equation that recovers thermal equilibrium and obeys energy conservation in the quark-coalescence process, while the fireball background is adjusted to hydrodynamic simulations of semicentral $\mathrm{Au}\text{−}\mathrm{Au}$ collisions at RHIC. To facilitate the applicability of the Langevin process, we focus on strange and charm quarks. Their interactions in the QGP are modeled using leading-order perturbative QCD augmented by effective Lagrangians with resonances that smoothly merge into hadronic states formed at $T_c$. The interaction strength is adjusted to reproduce the empirical saturation value for the quark-elliptic flow, $v_{2,q}^{\mathrm{sat}}\simeq 7\text{−}8\%$. The resulting ϕ and $J/\psi$ elliptic flow recover CQNS over a large range in transverse momentum ($p_T$) within a few percent. As a function of transverse kinetic energy, both the quark spectra from the Langevin simulations and the meson spectra generated via resonance recombination recover CQNS from zero to at least $3\hspace{0.5em}\mathrm{GeV}$.

Figure 1

$p_T$ spectra for ϕ mesons using the Boltzmann recombination equation in the equilibrium limit, Eq. (7), based on blast-wave input distributions for strange quarks (solid line), compared to ϕ spectra directly obtained from a blast-wave expression with the same fireball parameters (temperature $T=180\hspace{0.5em}\mathrm{MeV}$, radial expansion surface velocity ${\beta }_0=0.55c$). The ϕ-meson resonance parameters are $m_{\varphi }=1.02\hspace{0.5em}\mathrm{GeV}$, ${\Gamma }_{\varphi }=50\hspace{0.5em}\mathrm{MeV}$, and the $s$-quark mass is $m_s=0.45\hspace{0.5em}\mathrm{GeV}$.

Figure 2

Quark $p_t$ distributions resulting from relativistic Langevin simulations of an expanding elliptic QGP fireball at the end of a QGP (mixed) phase at a temperature of $T=180\hspace{0.5em}\mathrm{MeV}$ and average radial surface expansion velocity, $\langle {\beta }_0\rangle \simeq 0.48c$. The numerically computed spectra (long-dashed lines) are compared to the initial spectra (solid lines) and to a blast-wave parametrization for particles with the same mass and the same fireball conditions ($T=180\hspace{0.5em}\mathrm{MeV}$ and the same flow field as used for the background medium in the Langevin simulation; short-dashed lines). Left and right panels correspond to charm ($m_c=1.5\hspace{0.5em}\mathrm{GeV}$) and strange ($m_s=0.45\hspace{0.5em}\mathrm{GeV}$) quarks, respectively.

Figure 3

Meson $p_T$ spectra from quark-antiquark coalescence in central $\sqrt{s_{\mathit{NN}}}=200\hspace{0.5em}\mathrm{GeV}\hspace{0.5em}\mathrm{Au}\text{−}\mathrm{Au}$ collisions computed within the resonance recombination model for $J/\psi$ (left panel) and ϕ (right panel); experimental data are from Refs. [36] and [37, 38, 39], respectively.

Figure 4

Scaled quark $v_2^{\mathrm{scaled}}$ (dashed lines) and meson $v_{2,M}$ (solid lines) coefficients as a function of meson $p_T$ for $J/\Psi (Q=0.1\hspace{0.5em}\mathrm{GeV},\Gamma =0.1\hspace{0.5em}\mathrm{GeV}$; left panel) and $\varphi (Q=0.12\hspace{0.5em}\mathrm{GeV},\Gamma =0.05\hspace{0.5em}\mathrm{GeV}$; right panel) mesons.

Figure 5

Elliptic flow coefficient, $v_2$, as a function of transverse momentum for $c$ and $s$ quarks (left panel), as well as $J/\psi$ and ϕ mesons resulting from quark recombination (right panel), in semicentral $\sqrt{s_{\mathit{NN}}}=200\hspace{0.5em}\mathrm{GeV}\hspace{0.5em}\mathrm{Au}\text{−}\mathrm{Au}$ collisions.

Figure 6

Elliptic flow coefficient, $v_2$, as a function of transverse kinetic energy, $K_{t,T}$, for strange and charm quarks (left panel), as well as for ϕ and $J/\psi$ mesons (right panel).