Factorization and transverse phase-space parton distributions

TL;DR

This paper develops a theoretical framework for impact-parameter dependent cross sections in high-energy collisions, deriving a factorization formula using effective theory and validating it with perturbative calculations.

Contribution

It introduces a new factorization formula for impact-parameter dependent cross sections using soft-collinear effective theory and models non-perturbative effects in heavy-ion collisions.

Findings

Derived a general impact-parameter dependent cross section formula.

Confirmed the formula matches the Glauber model for heavy-ion collisions.

Verified the formula at one-loop order for Drell-Yan processes.

Abstract

We first revisit impact-parameter dependent collisions of ultra-relativistic particles in quantum field theory. Two conditions sufficient for defining an impact-parameter dependent cross section are given, which could be violated in proton-proton collisions. By imposing these conditions, a general formula for the impact-parameter dependent cross section is derived. Then, using soft-collinear effective theory, we derive a factorization formula for the impact-parameter dependent cross section for inclusive hard processes with only colorless final-state products in hadron and nuclear collisions. It entails defining thickness beam functions, which are Fourier transforms of transverse phase-space parton distribution functions. By modelling non-perturbative modes in thickness beam functions of large nuclei in heavy-ion collisions, the factorization formula confirms the cross section in the Glauber model for hard processes. Besides, the factorization formula is verified up to one loop in perturbative QCD for the inclusive Drell-Yan process in quark-antiquark collisions at a finite impact parameter.