Rapidity divergences and valid definitions of parton densities

Abstract

Rapidity divergences occur when parton densities in a gauge theory are defined in the most natural way, as expectation values of partonic number operators in light-front quantization. I review these and other related divergences, and show how the definitions of parton densities can be modified to remove the divergences. A modified definition is not only essential for many phenomenological applications of QCD, but also concerns the treatment of parton densities in non-perturbative approaches. The necessity of modifications in the definition of a parton density also entails corrections in the formulation of light-front quantization for gauge theories.

9 pages. To appear in Proceedings of LIGHT CONE 2008

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• Lorentz invariance relations between parton distributions and the Wandzura-Wilczek approximation
• Jets in the forward region at the LHC
• Transversity and T-odd PDFs from Drell-Yan processes with $pp$, $pD$ and $DD$ collisions
• Renormalization-group anatomy of transverse-momentum dependent parton distribution functions in QCD
• Gauge links, TMD-factorization, and TMD-factorization breaking
• Multiparton interactions and multiparton distributions in QCD
• New results on gauge-invariant TMD PDFs in QCD
• Anomalous dimensions of transverse-momentum dependent parton distribution functions
• Studies of forward jets and production of W, Z bosons at LHC energies
• QCD Beyond Leading Power
• Theory Summary of the Hadron Structure and QCD Workshop 2008