Document Type


Publication Date




Publication Title

Physical Review D






074031 (1-34)


The factorization theorems of QCD apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress testing the limits of the factorization program and for examining general properties of the parton density functions or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering and semi-inclusive deep inelastic scattering cross sections. In the case of semi-inclusive deep inelastic scattering, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent parton density functions are needed, from a purely collinear large transverse momentum region, and we examine the influence of subleading power corrections. We also review the steps for formulating transverse momentum dependent factorization in transverse coordinate space, and we study the effect of transforming to the well-known b scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model approach and compare it with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.


Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Original Publication Citation

Aslan, F., Gamberg, L., Gonzalez-Hernandez, J. O., Rainaldi, T., & Rogers, T. C. (2023). Basics of factorization in a scalar Yukawa field theory. Physical Review D, 107(7), 1-34, Article 074031.


0000-0002-0762-0275 (Rogers)