Shear viscosity of a hadron gas and influence of resonance lifetimes on relaxation time

Abstract

We address a discrepancy between different computations of η/s (shear viscosity over entropy density) of hadronic matter. Substantial deviations of this coefficient are found between transport approaches mainly based on resonance propagation with finite lifetime and other (semi-analytical) approaches with energy-dependent cross-sections, where interactions do not introduce a timescale. We provide an independent extraction of this coefficient by using the newly-developed SMASH (Simulating Many Accelerated Strongly interacting Hadrons) transport code, which is an example of a mainly resonance-based approach. We compare the results from SMASH with numerical solutions of the Boltzmann equation for simple systems using the Chapman-Enskog expansion, as well as previous results in the literature. Our conclusion is that the hadron interaction via resonance formation/decay strongly affects the transport properties of the system, resulting in significant differences in η/s with respect to other approaches where binary collisions dominate. We argue that the relaxation time of the system -which characterizes the shear viscosity-is determined by the interplay between the mean-free time and the lifetime of resonances. We show how an artificial shortening of the resonance lifetimes, or the addition of a background elastic cross section nicely interpolate between the two discrepant results. arXiv:1709.03826v1 [nucl-th]

Transport coefficients for multicomponent gas of hadrons using Chapman-Enskog method

“…Similarly, compared to models like ideal hadron resonance gas, excluded volume approach [37][38][39][40][41] which uses constant values of cross-section, the present formalism utilizes the energy dependence of crosssections to calculate the temperature dependence of transport coefficients. Calculations of shear viscosity has also been done using the Kubo formalism in transport models [42,43]. Our results on transport coefficients are in reasonable agreement with that from the transport models in the temperature range of T = 80 − 110 MeV.…”

Electrical conductivity and relaxation via colored noise in a hadronic gas

“…Thus we follow the path started in our previous works, Refs. [21][22][23] focusing on shear viscosity, but now compute the electrical conductivity. Since SMASH constitutes a good description of various experimental data, like hadron properties and cross sections (see [13,24] for more details, and [25,26] for on-line examples of its performance), the value of the transport coefficients extracted in this work can be seen as a result restricted by experiment.…”

“…As observed in our previous study, Refs. [21,22], the lifetimes of the formed resonances might influence the relaxation of the fluctuations, affecting the transport coefficient at high temperatures. This is an important dynamical feature of the propagating resonances, which is absent in all previous studies based on semianalytical solutions of transport equations.…”

van der Waals hadron resonance gas and QCD phase diagram

“…However, there have been some studies [35,46,47] on η/s of hadron gas as a function of temperature and baryon chemical potential, covering a wide range in the QCD (T , μ B ) plane. In this phenomenological study, we calculate η for the VDWHRG gas following an analytical formula as adopted in Ref.…”

“…The transport coefficient of hadron gas is studied using the relaxation time approximation (RTA) [44,45], also. The temperature dependence of η/s for hadronic matter at zero μ B , estimated in microscopic transport calculations [46,47] with UrQMD and (conceptually similar) SMASH, employing Kubo formalism, result in considerably different values of η/s at low temperature. The variance in the values of η/s from various transport models can be attributed [47] to varied microscopic details that can be translated very differently into macroscopic effects.…”