Viscous corrections to anisotropic flow and transverse momentum spectra from transport theory

TL;DR

This paper derives viscous corrections to anisotropic flow and transverse momentum spectra from transport theory, highlighting dependencies on microscopic interactions and initial conditions, and comparing with viscous hydrodynamics.

Contribution

It provides the first-order viscous correction to flow and spectra from transport calculations, revealing limitations of standard viscous hydrodynamics in describing high-$p_T$ behavior.

Findings

Viscous correction to flow increases with $p_T$ but more slowly than hydrodynamics predicts.

Dependence of spectra correction on initial momentum distribution is significant.

Linear response coefficient $v_n(p_T)/ ext{epsilon}_n$ is nearly independent of $n$ in ideal limit.

Abstract

Viscous hydrodynamics is commonly used to model the evolution of the matter created in an ultra-relativistic heavy-ion collision. It provides a good description of transverse momentum spectra and anisotropic flow. These observables, however, cannot be consistently derived using viscous hydrodynamics alone, because they depend on the microscopic interactions at freeze-out. We derive the ideal hydrodynamic limit and the first-order viscous correction to anisotropic flow ($v_2$, $v_3$ and $v_4$) and momentum spectrum using a transport calculation. The linear response coefficient to the initial anisotropy, $v_n(p_T)/\varepsilon_n$, depends little on $n$ in the ideal hydrodynamic limit. The viscous correction to the spectrum depends not only on the differential cross section, but also on the initial momentum distribution. This dependence is not captured by standard second-order viscous hydrodynamics. The viscous correction to anisotropic flow increases with $p_T$, but this increase is slower than usually assumed in viscous hydrodynamic calculations. In particular, it is too slow to explain the observed maximum of $v_n$ at $p_T\sim 3$ GeV/c.