Particle number diffusion in second-order relativistic dissipative hydrodynamics with momentum-dependent relaxation time

This article explores particle number diffusion in relativistic hydrodynamics using kinetic theory with a modified collision kernel that incorporates the momentum dependence of the particle relaxation time. Starting from the Boltzmann equation within the extended relaxation time approximation (ERTA), we derive second-order evolution equations for the dissipative number current and calculate the associated transport coefficients. The sensitivity of transport coefficients to the particle momentum dependence of the collision time scale of the microscopic interactions in the hot QCD medium is analyzed. For a conformal, number-conserving system, we compare the ERTA-modified transport coefficients for particle diffusion with exact results derived from scalar field theory. With an appropriate parameterization of the relaxation time, we demonstrate the consistency of our analysis and assess the degree of agreement of the results with the exact solutions from scalar field theory. The relaxation times for the shear and number diffusion evolution equations are seen to be distinct in general when the momentum dependence of the relaxation time is taken into consideration.