Collinear Approximations for LHC Cross Sections: Factorization and Resummation

TL;DR

This paper develops a collinear approximation framework for LHC cross sections, enabling improved predictions for color singlet production by resumming relevant logarithms and analyzing approximation accuracy.

Contribution

It introduces a factorization theorem for collinear radiation in color singlet production, extending resummation techniques beyond threshold approximations.

Findings

The approximation accurately predicts cross sections in tested scenarios.

Resummation to NNLL' accuracy improves theoretical precision.

The framework extends the applicability of resummation methods.

Abstract

We explore a factorization theorem for color singlet production cross sections at the LHC in the limit of additional radiation becoming collinear to the direction of either of the colliding protons. The resulting formula approximates the cross section as a function of the Born variables of the color singlet final state, specifically its mass and rapidity. We analyze the quality of this approximation and study its limitations at the example of gluon-fusion Higgs boson production and Drell-Yan production through next-to-next-to-leading order in QCD perturbation theory. Furthermore, we resum logarithms enhanced in the collinear limit to next-to-next-to-next-to-leading logarithmic accuracy for our two example processes. We conclude that this framework of collinear approximation is a natural successor to the threshold approximation and resummation for inclusive and differential observables in color-neutral processes.