  We compute the mean free path and shear viscosity in the color-flavor locked
(CFL) phase of dense quark matter at low temperature T, when the contributions
of mesons, quarks and gluons to the transport coefficients are Boltzmann
suppressed. CFL quark matter displays superfluid properties, and transport
phenomena in such cold regime are dominated by phonon-phonon scattering. We
study superfluid phonons within thermal field theory and compute the mean free
path associated to their most relevant collision processes. Small-angle
processes turn out to be more efficient in slowing transport phenomena in the
CFL matter, while the mean free path relevant for the shear viscosity is less
sensitive to collinear scattering due to the presence of zero modes in the
Boltzmann equation. In analogy with superfluid He4, we find the same T power
law for the superfluid phonon damping rate and mean free path. Our results are
relevant for the study of rotational properties of compact stars, and correct
wrong estimates existing in the literature.
