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

TL;DR

This paper develops a factorization theorem within Soft-Collinear Effective Theory for Higgs boson transverse momentum and rapidity distributions at hadron colliders, enabling systematic resummation of large logarithms and higher order corrections.

Contribution

It introduces a universal factorization framework in SCET for Higgs differential distributions, including novel impact-parameter beam functions and inverse soft functions, simplifying higher order calculations.

Findings

Derived formulas for factorization in momentum and impact parameter space.

Summed large logarithms using renormalization group equations.

Validated the theorem through consistency checks and comparison with fixed order QCD results.

Abstract

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.