Next-to-leading order QCD corrections to differential distributions of Higgs boson production in hadron-hadron collisions

We present the full next-to-leading order corrected differential distributions $d^2\sigma/dp_T/dy$, $d\sigma/dp_T$ and $d\sigma/dy$ for the semi-inclusive process $p + p\to H + 'X'$. Here $X$ denotes the inclusive hadronic state and $p_T$ and $y$ are the transverse momentum and rapidity of the Higgs-boson $H$ respectively. All QCD partonic subprocesses have been included. The computation is carried out in the limit that the top-quark mass $m_t \to \infty$ which is a very good approximation as long as $m_H,p_T < 200$ GeV. Our calculations reveal that the dominant subprocess is given by $g + g \to H + 'X'$ but the reaction $g + q(\bar q) \to H + 'X'$ is not negligible. Another feature is that the $K$-factor representing the ratio between the next-to-leading order and leading order differential distributions is large. It varies from 1.4 to 1.7 depending on the kinematic region and choice of parton densities. We show that a reliable determination of the differential cross sections requires good knowledge of the gluon density in the region where $x < 10^{-3}$. Further we study whether the differential distributions are dominated at large transverse momentum by soft-plus-virtual gluon contributions. This is of interest for the resummation of large corrections which occur near the boundary of phase space. We also compare our results with those previously reported in the literature.