  By means of the field-theoretic renormalization group, we study the damping
of the viscosity coefficient near the superfluid phase transition. We utilize
the fact that in the infrared region, the complex model used to describe the
phase transition belongs to the same universality class as the well-known
stochastic model A. This allows us a determination of the critical behavior of
viscosity using composite operators for model A. Our analysis is based on the
$\varepsilon$-expansion near the upper critical dimension $d_c = 4$ of model A.
The critical exponent of viscosity is then calculated from the critical
dimensions of composite operators of massless two-component model A. In
particular, we present results for critical dimensions of a selected class of
composite operators with the canonical dimension $8$ to the leading order.
