  We study Higgs boson production from gluon-gluon fusion at mid-rapidity in
high energy proton-nucleus collisions. For this process the presently still
little known gluon distribution function $h_1^{\perp g}$ gives a numerically
relevant contribution. We show by explicite calculation that using CGC (color
glass condensate) model input the result obtained in the naive k_t
factorization approach matches the result obtained in the TMD factorization
framework for a dilute medium. We also verify the earlier finding that the k_t
factorization formalism for Higgs production breaks down in a dense medium. In
doing so we formulate a hybrid model which allows one to treat such reactions
theoretically.
