Estimating transport coefficients of interacting pion gas with K-matrix cross sections

Abstract

We estimate the transport coefficients, viz., shear and bulk viscosities as well as thermal and electrical conductivities, of hot pionic matter using relativistic Boltzmann equation in relaxation time approximation. We use K-matrix parametrization of pion-pion cross sections to estimate the transport coefficients which incorporate multiple heavy resonances while simultaneously preserving the unitarity of S-matrix. We compare transport coefficients estimated using K-matrix parametrization with existing literature on pionic transport coefficients. We find that the K-matrix scheme estimations are in reasonable agreement with previous results.

Hadron resonance gas with repulsive mean field interaction: Thermodynamics and transport properties

“…Further, η/s obtained using AdS/CFT correspondence [48] has put the lower bound on its value equal to 1 4π called the Kovtun-Son-Starinets (KSS) bound. This interesting finding has motivated many theoretical investigations of this ratio to understand and derive rigorously from a microscopic theory [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. The bulk viscosity coefficient (ζ) has also been realized to be important to be included the dissipative hydrodynamics.…”

Hadronic transport coefficients from the linear σ model at finite temperature

“…Rigorous quantitative control of the electrical conductivity can thereby also provide constraints on the phenomenology of soft electromagnetic radiation. The electrical conductivity has been the subject of previous studies with both hadronic (confined) and partonic degrees of freedom [13,[39][40][41][42][43][44][45][46][47]. The dc electrical conductivity was not previously studied in the LSM, although its vector structure is conducive to calculation using the variational method we have extended.…”

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

“…where the relativistic version of Gibbs-Duhem relation [47] T ∇ µ (µ/T ) = −w(∇ µ T /T − ∇ µ P/wn) was used for the derivation of Eq. (36).…”

“…In the present section we derive the transport coefficients for a single component system as described by the transport equation given in Eq. (36).…”

“…In regards to other formalism for e.g in Refs. [22,35,36], which uses relaxation time approximation (RTA), the present formalism is better in the sense that small angle scattering is taken care of naturally, where as RTA uses thermal averaged cross-sections. 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.…”