  We investigate the gluon distribution functions and their contributions to
the Higgs boson production in pp collisions in the transverse momentum
dependent factorization formalism. In addition to the usual azimuthal symmetric
transverse momentum dependent gluon distribution, we find that the azimuthal
correlated gluon distribution also contributes to the Higgs boson production.
This explains recent findings on the additional contribution in the transverse
momentum resummation for the Higgs boson production as compared to that for
electroweak boson production processes. We further examine the small-x naive
k_t-factorization in the dilute region and find that the azimuthal correlated
gluon distribution contribution is consistently taken into account, and the
result agrees with the transverse momentum dependent factorization formalism.
We comment on the possible breakdown of the naive k_t-factorization in the
dense medium region, due to the unique behaviors for the gluon distributions.
