  We present next-to-next-to-leading-order (NNLO) results for an exclusive soft
function that appears in a recently developed factorization theorem for
transverse momentum distributions. The factorization theorem, derived using the
Soft Collinear Effective Theory, involves both a soft function and unintegrated
nucleon distribution functions fully differential in momentum coordinates. The
soft function is given by the vacuum matrix element of soft Wilson lines and is
also fully differential in all components. We give results and relevant
technical details for the NNLO calculation of the soft function, including
finite parts, and derive the corresponding anomalous dimension. These results
are necessary for achieving low transverse momentum resummation at
next-to-next-to-leading-logarithmic accuracy in this effective field theory
approach with unintegrated distribution functions.
