We derive a factorization theorem for the Higgs boson transverse momentum ($p_T$) and rapidity ($Y$) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for $m_h\gg p_T\gg {\Lambda }_{\mathrm{QCD}}$, where $m_h$ denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the $p_T$ scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the $p_T$-scale physics simplifies the implementation of higher order radiative corrections in ${\alpha }_s(p_T)$. We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in $p_T/m_h$ and ${\Lambda }_{\mathrm{QCD}}/p_T$ can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-$p_T$ resummation.

• Received 18 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.093007