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In the production of the Higgs through a bottom-quark loop, the transversemomentum distribution of the Higgs at large $P_T$ is complicated by itsdependence on two other important scales: the bottom quark mass $m_b$ and theHiggs mass $m_H$. A strategy for simplifying the calculation of the crosssection at large $P_T$ is to calculate only the leading terms in its expansionin $m_b^2/P_T^2$. In this paper, we consider the bottom-quark-loop contributionto the parton process $q\bar{q}\to H+g$ at leading order in $\alpha_s$. We showthat the leading power of $1/P_T^2$ can be expressed in the form of afactorization formula that separates the large scale $P_T$ from the scale ofthe masses. All the dependence on $m_b$ and $m_H$ can be factorized into adistribution amplitude for $b \bar b$ in the Higgs, a distribution amplitudefor $b \bar b$ in a real gluon, and an endpoint contribution. The factorizationformula can be used to organize the calculation of the leading terms in theexpansion in $m_b^2/P_T^2$ so that every calculation involves at most twoscales.

Mass Dependence of Higgs Production at Large Transverse Momentum through a Bottom Quark Loop