Sudakov double logarithms resummation in hard processes in the small-xsaturation formalism

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.