Gluon distribution functions and Higgs boson production at moderate transverse momentum

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 kₜ-factorization in the dilute region and find that the azimuthal correlated gluon distribution contribution is consistently taken into account. The result agrees with the transverse momentum-dependent factorization formalism. We comment on the possible breakdown of the naive kₜ-factorization in the dense medium region, due to the unique behaviors for the gluon distributions.