Quasiparticle anisotropic hydrodynamics for central collisions

We use quasiparticle anisotropic hydrodynamics to study an azimuthally symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state (EoS). We compare results obtained by using the quasiparticle method with the standard method of imposing the EoS in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spectra, total number of charged particles, and average transverse momentum for various values of the shear viscosity to entropy density ratio $\eta /s$. We find that the three methods agree well for small shear viscosity to entropy density ratio $\eta /s$, but differ at large $\eta /s$, with the standard anisotropic EoS method showing suppressed production at low transverse-momentum compared with the other two methods considered. Finally, we demonstrate explicitly that, when using standard viscous hydrodynamics, the bulk-viscous correction can drive the primordial particle spectra negative at large $p_T$. Such behavior is not seen in either anisotropic hydrodynamics approach, irrespective of the value of $\eta /s$.

Figure 1

Comparison of the neutral pions, kaons ($K^{+}$), and protons spectra as a function of transverse momentum $p_T$ obtained by using aHydroQP, aHydro, and vHydro. The shear viscosity to entropy density ratio is $4\pi \eta /s=1$.

Figure 2

Same as Fig. 1, except here the shear viscosity to entropy density ratio was taken to be $4\pi \eta /s=3$.

Figure 3

Same as Fig. 1, except here the shear viscosity to entropy density ratio was taken to be $4\pi \eta /s=10$.

Figure 4

Comparison of the total number of pions (${\pi }^0$), kaons ($K^0$), and protons as a function of $4\pi \eta /s$ obtained by using aHydroQP, aHydro, and vHydro.

Figure 5

Comparison of the neutral pion, kaon ($K^{+}$), and proton average transverse momentum as a function of $4\pi \eta /s$ obtained by using aHydroQP, aHydro, and vHydro.

Figure 6

The number of total charged particles as a function of $4\pi \eta /s$ obtained by using aHydroQP, aHydro, and vHydro.

Figure 7

Comparisons of the $p$-Pb neutral pion, kaon ($K^{+}$), and proton spectra as a function of transverse momentum $p_T$ obtained by using aHydroQP, aHydro, and vHydro. The shear viscosity to entropy density ratio is $4\pi \eta /s=1$.

Figure 8

Same as Fig. 7, except here the shear viscosity to entropy density ratio was taken to be $4\pi \eta /s=3$.