On the Drell–Levy–Yan relation to O(α2)

2000/04/18 by J. Blümlein, V. Ravindran, W. L. van Neerven +1 · 6 citations
Mathematics · Physics and Astronomy · #Annihilation #Deep inelastic scattering #Fragmentation (computing) #Geometry #High-Energy Particle Collisions Research #Inelastic scattering #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Parton #Perturbative QCD #Photon #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Scaling #Scattering #hep-ex #hep-ph

paper · pdf · doi:10.1016/s0550-3213(00)00422-3

published as Nucl.Phys. B586 (2000) 349-381 · 33 pages LATEX, 1 style file

arxiv created 2000/04/18 · openalex publication_date 2000/10/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

We study the validity of a relation by Drell, Levy and Yan (DLY) connecting the deep inelastic structure (DIS) functions and the single-particle fragmentation functions in e⁺e^- annihilation which are defined in the spacelike (q²<0) and timelike (q²>0) regions respectively. Here q denotes the momentum of the virtual photon exchanged in the deep inelastic scattering process or the annihilation process. An extension of the DLY-relation, which originally was only derived in the scaling parton model, to all orders in QCD leads to a connection between the two evolution kernels determining the q²-dependence of the DIS structure functions and the fragmentation functions respectively. In relation to this we derive the transformation relations between the space-and time-like splitting functions up to next-to-leading order (NLO) and the coefficient functions up to NNLO both for unpolarized and polarized scattering. It is shown that the evolution kernels describing the combined singlet evolution for the structure functions F₂(x,Q²), F_L(x,Q²) where Q²=|q²| or F₂(x,Q²), ∂ F₂(x,Q²)/∂ ln(Q²) and the corresponding fragmentation functions satisfy the DLY relation up to next-to-leading order. We also comment on a relation proposed by Gribov and Lipatov.

Citations

• Asymptotic freedom in parton language
• The infrared divergence phenomena and high-energy processes
• Degenerate Systems and Mass Singularities
• A Relativistic Equation for Bound-State Problems
• Note on the Radiation Field of the Electron
• NNLO evolution of deep-inelastic structure functions: the non-singlet case

Cited by

• NNLO splitting and coefficient functions with time-like kinematics
• Algebraic relations between harmonic sums and associated quantities
• Quark distributions of octet baryons from SU(3) symmetry
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• Collinear limit of the energy-energy correlator
• Subleading logarithmic QED initial state corrections to e+e−→γ⁎/Z0⁎ to O(α6L5)