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

Abstract

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.

arXiv comment32 pages, 3 figures. This is the final version

References in corpus (27)

• Parton Physics on Euclidean Lattice
• Final state interactions and gauge invariant parton distributions
• Analyticity in Spin in Conformal Theories
• Universality of soft and collinear factors in hard-scattering factorization
• Structure functions for large $x$ and renormalization of Wilson loops
• Factorization at the LHC: From PDFs to Initial State Jets
• Large-Momentum Effective Theory
• Causality Constraints in Conformal Field Theory
• Resolution of singularities for multi-loop integrals
• Soft-/rapidity- anomalous dimensions correspondence
• Feynman graph polynomials
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• TMD Soft Function from Large-Momentum Effective Theory
• Transverse-Momentum-Dependent Parton Distribution Functions from Large-Momentum Effective Theory
• Transverse Momentum Dependent Quasi-Parton-Distributions
• Energy correlations in the end-point region
• Self-contained definition of the Collins-Soper kernel
• The Transverse Momentum Dependent Fragmentation Function at NNLO
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel
• Lattice Heavy Quark Effective Theory and the Isgur-Wise function
• Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
• Consistency and lattice renormalization of the effective theory for heavy quarks
• Soft factors for double parton scattering at NNLO
• Moving NRQCD for heavy-to-light form factors on the lattice
• Conformal Regge Theory at Finite Boost