One-loop Matching for Spin-Dependent Quasi-TMDs

Abstract

Transverse momentum dependent parton distribution functions (TMDPDFs) provide a unique probe of the three-dimensional spin structure of hadrons. We construct spin-dependent quasi-TMDPDFs that are amenable to lattice QCD calculations and that can be used to determine spin-dependent TMDPDFs. We calculate the short-distance coefficients connecting spin-dependent TMDPDFs and quasi-TMDPDFs at one-loop order. We find that the helicity and transversity distributions have the same coefficient as the unpolarized TMDPDF. We also argue that the same is true for pretzelosity and that this spin universality of the matching will hold to all orders in ${\alpha }_s$. Thus, it is possible to calculate ratios of these distributions as a function of longitudinal momentum and transverse position utilizing simpler Wilson line paths than have previously been considered.

24 pages, 4 figures

References in corpus (5)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T
• SCET, Light-Cone Gauge and the T-Wilson Lines
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations