  In this paper, using the Higgs production in forward rapidity region in
proton-nucleus collisions as an example, we demonstrate that we can construct a
systematic formalism for the threshold resummation for forward rapidity
particle productions in the saturation formalism. The forward threshold jet
function, which satisfies the corresponding renormalization group equation, is
introduced into the new factorization formula. This calculation can be easily
generalized to other processes, such as single forward hadron productions at
forward rapidity region, and have important phenomenological implications.
