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Neutrino diffusive transport in hot quark matter: a detailed analysis

We perform an extensive analysis of neutrino diffusion in quark matter within the MIT bag model at arbitrary temperature and degeneracy. We examine in detail the contribution of each of the relevant weak interaction processes to the total neutrino opacity and evaluate the effect of the strange quark mass, the bag constant, and the QCD perturbative corrections to the MIT bag model. We also investigate the anisotropic contribution to the neutrino distribution function in scatterings, the mean energy transfer and the mean scattering angle. The density and temperature dependence of the diffusion coefficients $D_n$ that govern the cooling and deleptonization of a compact star is shown in detail. Finally, our numerical results for the neutrino mean free paths are compared against known analytic approximations. We conclude that neutrino scattering constitutes a significant portion of the total neutrino opacity in leptonized quark matter and neutrino-quark scattering is, in general, very similar to neutrino-electron scattering with respect to both mean energy transfer per scattering and mean scattering angle.