Matching factorization theorems with an inverse-error weighting

TL;DR

The paper introduces a new, efficient method for matching factorization theorems in different kinematic regions in QCD, using inverse-error weighting based on theoretical uncertainties, improving upon existing subtraction schemes.

Contribution

A novel inverse-error-weighted approach for matching factorization theorems that simplifies calculations and provides uncertainty estimates, applicable to various differential cross sections.

Findings

Method performs well compared to Collins-Soper-Sterman scheme

Applicable to multiple processes like Z, W, H boson production and Drell-Yan

Can be extended to other variables and multi-differential measurements

Abstract

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as $Z$ boson, $W$ boson, $H^0$ boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.