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

We present a fully analytic calculation of the Higgs boson transverse momentum and rapidity distributions, for nonzero Higgs $p_{\perp }$, at next-to-leading order in the infinite-top-mass approximation. We separate the cross section into a part that contains the dominant soft, virtual, collinear, and small-$p_{\perp }$-enhanced contributions, and the remainder, which is organized by the contributions due to different parton helicities. We use this cross section to investigate analytically the small-$p_{\perp }$ limit and compare with the expectation from the resummation of large logarithms of the type $\ln m_H\mathrm{/}{p}_{\perp }$. We also compute numerically the cross section at moderate $p_{\perp }$ where a fixed-order calculation is reliable. We find a $K$-factor that varies from $\approx 1.6-1.8$, and a reduction in the scale dependence, as compared to leading order. Our analysis suggests that the contribution of current parton distributions to the total uncertainty on this cross section at the LHC is probably less than that due to uncalculated higher orders.