Basics of factorization in a scalar Yukawa field theory

Abstract

The factorization theorems of quantum chromodynamics (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 (pdfs) 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 (DIS) and semi-inclusive deep inelastic scattering (SIDIS) cross sections. In the case of SIDIS, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent (TMD) pdfs 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 TMD factorization in transverse coordinate space, and we study the effect of transforming to the well-known $b_{\ast }$-scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model (GPM) approach, and compare with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.

39 pages, 46 figures

References in corpus (23)

• Transverse-momentum distributions in a diquark spectator model
• Parton distributions and lattice QCD calculations: toward 3D structure
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
• Origin of single transverse-spin asymmetries in high-energy collisions
• Unpolarized Transverse Momentum Distributions from a global fit of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering data
• Evidence for intrinsic charm quarks in the proton
• Process dependent Sivers function and implications for single spin asymmetry in inclusive hadron production
• Transverse momentum dependent operator expansion at next-to-leading power
• Updated QCD global analysis of single transverse-spin asymmetries I: Extracting $\tilde{H}$, and the role of the Soffer bound and lattice QCD
• Can $\overline{\mathrm{MS}}$ parton distributions be negative?
• Positivity and renormalization of parton densities
• Role of the Soffer bound in determination of transversity and the tensor charge
• Parton distributions need representative sampling
• A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes
• Predictive power of transverse-momentum-dependent distributions
• Pathologies of the KMR prescriptions for unintegrated PDFs: Which prescription should be preferred?
• Combining nonperturbative transverse momentum dependence with TMD evolution
• Intrinsic Transverse Momentum and Evolution in Weighted Spin Asymmetries
• On the normalization of unintegrated parton densities
• Transverse moments of TMD parton densities and ultraviolet divergences
• Collinear Factorization at sub-asymptotic kinematics and validation in a diquark spectator model
• Quark-model relations among TMDs in the parton model

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