Factorization and transverse phase-space parton distributions

• Published in: The journal of high energy physics Vol. 2021; no. 7; pp. 1 - 29
• Main Author: Wu, Bin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer Nature B.V; SpringerOpen
• Subjects: Atomic collisions; Classical and Quantum Gravitation; Cross-sections; Distribution functions; Effective Field Theories; Elementary Particles; Factorization; Field theory; Fourier transforms; Heavy ions; High energy physics; Ionic collisions; Mathematical models; Parameters; Particle collisions; Partons; Perturbative QCD; Physics; Physics and Astronomy; Protons; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativistic particles; Relativity Theory; String Theory; Thickness; Effective Field Theories; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2021)002

A bstract 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.