Phenomenological predictions of 3+1d anisotropic hydrodynamics

Abstract

We make phenomenological predictions for particle spectra and elliptic flow in heavy-ion collisions using 3+1d anisotropic hydrodynamics (aHydro) including the effects of both shear and bulk viscosities. The dynamical equations necessary are derived by taking moments of the Boltzmann equation allowing for three distinct (diagonal) momentum-space anisotropy parameters. The formulation is based on relaxation-time approximation for the collisional kernel and a lattice-QCD-based equation of state. Evolving the system to late times, we calculate particle production using THERMINATOR 2, modified to account for an ellipsoidal distribution function. We obtain particle spectra for different particle species such as pions, kaons, and protons, and elliptic flow $v_2$ as a function of centrality, transverse momentum, and rapidity. In our model, we have four free parameters, i.e. freeze-out temperature, initial central energy density, initial momentum-space anisotropies, and shear viscosity to entropy density ratio. Using a multidimensional fit to LHC experimental data, we make a preliminary extraction of these parameters. We find reasonable agreement between 3+1d aHydro and available experimental data for $η/s\sim 0.23$.