On Rapidity Divergences in the Soft and Collinear Limits of QCD

Abstract

We consider the definition of a transverse-momentum-dependent parton distribution function (TMDPDF) and its evolution properties given a factorization theorem of Drell- Yan lepton pair production with a non-vanishing transverse momentum. We discuss rapidity divergences that exist in both limits of QCD: the soft and collinear. We argue that only when a specific combination of the soft and collinear matrix elements is formed, rapidity divergences cancel. We also argue that the soft matrix element, calculated in perturbation theory, contains only rapidity divergences and there is no genuine long-distance infra-red divergences.

11 pages, 5 figures. To appear in proceedings of QCD Evolution workshop 2013

References in corpus (4)

• Parton distributions for the LHC
• Sivers Effect for Pion and Kaon Production in Semi-Inclusive Deep Inelastic Scattering
• Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions
• The QCD Evolution of the Sivers Function

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• The Universal Transverse Momentum Dependent Soft Function at NNLO
• TMD evolution and the Higgs transverse momentum distribution
• Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization
• Transverse momentum dependent operator expansion at next-to-leading power
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• Piecewise Linear Wilson lines
• Precision DIS data and TMD parton distributions