Factorization and Resummation of Higgs Boson Differential Distributions in Soft-Collinear Effective Theory

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>> p_T>> \Lambda_{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_{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.Comment: 66 pages, 5 figures, discussion regarding zero-bin subtractions adde

Erratum to the paper "A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension"

This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak factorization theorem for toroidal birational morphisms in [AMR], in the form utilized in [AKMR] for the proof of the weak factorization theorem for general birationla maps, avoiding the use of the above mentioned algorithm for the strong factorization, and 3. a list of corrections for a few other mistakes in [AMR], mostly pointed out by Laurent Bonavero.Comment: 3 page

Factorization theorem for high-energy scattering near the endpoint

A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the infrared divergences appear only in the parton distribution functions by carefully reorganizing collinear and soft parts. The central idea is extracting the soft contributions from the collinear part to avoid double counting. Combining it with the original soft part, an infrared-finite kernel is obtained. This factorization procedure can be applied to various high-energy scattering processes.Comment: 4 pages, version published in PR