Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities

• Published in: The journal of high energy physics Vol. 2024; no. 9; pp. 30 - 32
• Main Author: Liu, Yizhuang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 06.09.2024; Springer Nature B.V; SpringerOpen
• Subjects: Causality; Classical and Quantum Gravitation; Correlation Functions; Elementary Particles; Equality; Euclidean geometry; Form factors; Higher-Order Perturbative Calculations; Light; Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; String Theory; Wilson, ’t Hooft and Polyakov loops; Wilson, ’t Hooft and Polyakov loops; Correlation Functions; Renormalization and Regularization; Higher-Order Perturbative Calculations
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2024)030

A bstract We show that as a result of causality-constrained coordinate space analyticity, the Drell-Yan-shape transverse-momentum dependent soft factor in the exponential regulator allows Euclidean-type parametric representations without cuts, to all orders in perturbation theory. Moreover, it is identical to another soft factor defined with a single time-ordering that has a natural interpretation as a space-like form factor. Furthermore, this relation continues to hold for a larger class of TMD soft factors that interpolate between three different rapidity regulators: the off-light-cone regulator, the finite light-front length regulator, and the exponential regulator.