Viscosity of meson matter

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We report a calculation of the shear viscosity in a relativistic multicomponent meson gas as a function of temperature and chemical potentials. We approximately solve the Uehling-Uhlenbeck transport equation of kinetic theory, appropriate for a boson gas, with relativistic kinematics. Since at low temperatures the gas can be taken as mostly composed of pions, with a fraction of kaons and etas, we explore the region where binary elastic collisions with at least one pion are the dominant scattering processes. Our input meson scattering phase shifts are fits to the experimental data obtained from chiral perturbation theory and the inverse amplitude method. Our results take the correct nonrelativistic limit (viscosity proportional to the square root of the temperature), show a viscosity of the order of the cube of the pion mass up to temperatures somewhat below that mass, and then a large increase due to kaons and etas. Our approximation may break down at even higher temperatures, where the viscosity follows a temperature power law with an exponent near 3.
©2004 The American Physical Society. The authors thank J. R. Peláez and A. Gómez Nicola for providing us with their SU(3) phase shifts and useful discussions, S. Santalla and F. J. Fernández for extensive checks and assistance, and D. Davesne for some interesting comments. This work was supported by grants FPA 2000-0956 and BFM 2002-01003 (Spain).
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