Light-Cone Singularities and Transverse-Momentum-Dependent Factorization at Twist-3

Abstract

We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of ${\alpha }_s$. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.

arXiv commentpresentation improved, references added. Published version

References in corpus (33)

• Time-reversal odd distribution functions in leptoproduction
• The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction
• QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
• Final state interactions and gauge invariant parton distributions
• Universality of T-odd effects in single spin and azimuthal asymmetries
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• Universality of soft and collinear factors in hard-scattering factorization
• QCD Factorization for Spin-Dependent Cross Sections in DIS and Drell-Yan Processes at Low Transverse Momentum
• Parton Distributions in Light-Cone Gauge: Where Are the Final-State Interactions?
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Infrared Factorization, Wilson Lines and the Heavy Quark Limit
• Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions
• Calculation of the transverse parton distribution functions at next-to-next-to-leading order
• Asymmetries in polarized hadron production in e^+e^- annihilation up to order 1/Q
• Parameterization of the quark-quark correlator of a spin-1/2 hadron
• Soft-/rapidity- anomalous dimensions correspondence
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production
• Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice
• Collins-Soper Equation for the Energy Evolution of Transverse-Momentum and Spin Dependent Parton Distributions
• Equality of Two Definitions for Transverse Momentum Dependent Parton Distribution Functions
• Drell-Yan Lepton Angular Distribution at Small Transverse Momentum
• Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T
• New observables in longitudinal single-spin asymmetries in semi-inclusive DIS
• Transverse Momentum Dependent Factorization for Quarkonium Production at Low Transverse Momentum
• SCET, Light-Cone Gauge and the T-Wilson Lines
• Light-cone divergence in twist-3 correlation functions
• Transverse momentum dependence of the angular distribution of the Drell-Yan process
• Twist-3 Single-Spin Asymmetries in Semi-Inclusive Deep-Inelastic Scattering
• Angular distribution of leptons from the decay of massive vector bosons
• TMD theory, factorization and evolution
• Transverse momentum dependent twist-three result for polarized Drell-Yan processes

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• Semi-Inclusive Deep Inelastic Scattering in Wandzura-Wilczek-type approximation
• The twist-three distribution $e^q(x,k_{\perp })$ in a light-front model
• Azimuthal asymmetries in unpolarized SIDIS and Drell-Yan processes: a case study towards TMD factorization at subleading twist
• Beam-helicity asymmetries for single-hadron production in semi-inclusive deep-inelastic scattering from unpolarized hydrogen and deuterium targets
• Evolution of unpolarized transverse momentum dependent parton distributions of twist-3