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

Abstract

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 $\mathrm{Au}\text{\ensuremath{-}}\mathrm{Au}$ 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, ${v}_{2,q}^{\mathrm{sat}}\ensuremath{\simeq}7\text{\ensuremath{-}}8%$. The resulting \ensuremath{\phi} and $J/\ensuremath{\psi}$ 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 $3 \mathrm{GeV}$.