Evolution of unpolarized transverse momentum dependent parton distributions of twist-3

Abstract

We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal{O}({\alpha }_s)$. Unlike the existing calculations in the literature, which are based on the background field method, we derive the evolution equations directly through diagram expansion. Additionally, instead of using the $\delta$ regulator, we employ the exponential regulator to regularize the rapidity divergences. We find that the evolutions of the four twist-3 TMD PDFs are governed by eight homogeneous equations. Our evolution kernels agree with one set of results in the literature, but differ from another by a sign. Considering the advantages of the exponential regulator in high-order perturbative calculations, our results are crucial for computing the twist-3 TMD PDFs at $\mathcal{O}({\alpha }_s^2)$.

31 pages, 5 figures, V3: Version published in PRD

References in corpus (40)

• The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction
• Semi-inclusive deep inelastic scattering at small transverse momentum
• 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
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• 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?
• Calculation of the quark and gluon form factors to three loops in QCD
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• The Rapidity Renormalization Group
• Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• 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
• Analytic Regularization in Soft-Collinear Effective Theory
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Transverse momentum dependent PDFs at N${}^3$LO
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions
• Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
• The Four Loop QCD Rapidity Anomalous Dimension
• 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 Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Transverse momentum dependent operator expansion at next-to-leading power
• TMD Fragmentation Functions at N${}^3$LO
• Azimuthal asymmetries in unpolarized SIDIS and Drell-Yan processes: a case study towards TMD factorization at subleading twist
• Transverse-momentum-dependent wave functions and Soft functions at one-loop in Large Momentum Effective Theory
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Transverse momentum dependent twist-three result for polarized Drell-Yan processes
• Light-Cone Singularities and Transverse-Momentum-Dependent Factorization at Twist-3
• Evolution of Chirality-odd Twist-3 Fragmentation Functions