  In this manuscript, we present a complete study of the Sudakov double
logarithms resummation for various hard processes in eA and pA collisions in
the small-x saturation formalism. We first employ a couple of slightly
different formalisms to perform the one-loop analysis of the Higgs boson
production process in pA collisions, and demonstrate that Sudakov-type
logarithms arise as the leading correction and that they can be systematically
resummed in addition to the usual small-x resummation. We further study the
Sudakov double logarithms for other processes such as heavy quark pair
production and back-to-back dijet production in eA and pA collisions through
detailed calculation of the corresponding one-loop diagrams. As the most
important contribution from the one-loop correction, the Sudakov factor should
play an important role in the phenomenological study of saturation physics in
the pA programs at RHIC and the LHC.
