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We present a fully analytic calculation of the Higgs boson transversemomentum and rapidity distributions, for nonzero Higgs $p_\perp$, atnext-to-leading order in the infinite-top-mass approximation. We separate thecross section into a part that contains the dominant soft, virtual, collinear,and small-$p_\perp$-enhanced contributions, and the remainder, which isorganized by the contributions due to different parton helicities. We use thiscross section to investigate analytically the small-$p_\perp$ limit and comparewith the expectation from the resummation of large logarithms of the type$\ln{m_H/p_\perp}$. We also compute numerically the cross section at moderate$p_\perp$ where a fixed-order calculation is reliable. We find a $K$-factorthat varies from $\approx1.6-1.8$, and a reduction in the scale dependence, ascompared to leading order. Our analysis suggests that the contribution ofcurrent parton distributions to the total uncertainty on this cross section atthe LHC is probably less than that due to uncalculated higher orders.Comment: 40 pages, 10 figures, JHEP style (minor changes, added reference

Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion