Mass dependence of Higgs boson production at large transverse momentum through a bottom-quark loop

In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large P-T is complicated by its dependence on two other important scales: the bottom quark mass m(b) and the Higgs mass m(H). A strategy for simplifying the calculation of the cross section at large P-T is to calculate only the leading terms in its expansion in m(b)(2)/P-T(2). In this paper, we consider the bottom-quark-loop contribution to the parton process q (q) over bar -> H + g at leading order in alpha(s). We show that the leading power of 1/P-T(2) can be expressed in the form of a factorization formula that separates the large scale PT from the scale of the masses. All the dependence on mb and mH can be factorized into a distribution amplitude for b (b) over bar in the Higgs, a distribution amplitude for b (b) over bar in a real gluon, and an end point contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in m(b)(2)/P-T(2) so that every calculation involves at most two scales.