Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The spin-dependent two-loop splitting functions

W. Vogelsang

TL;DR

The paper delivers a thorough calculation of spin-dependent next-to-leading order splitting functions in QCD using the light-cone gauge, detailing how gamma5 and Levi-Civita contractions are handled across schemes. It provides complete HVBM-based results and examines alternative gamma5 prescriptions, demonstrating that suitable scheme transformations align those results with prior OPE-based findings (MVN). A clear link to dimensional reduction is established, showing how finite counterterms and mass-singularity differences map between schemes and preserve essential supersymmetric-like relations. This work enables accurate NLO QCD evolution of polarized parton densities and offers robust cross-checks for spin-dependent DIS analyses.

Abstract

We present a complete description of the calculation of the spin-dependent next-to-leading order splitting functions. The calculation is performed in the light-cone gauge. We give results for different prescriptions for the Dirac matrix $γ_5$ in $d=4-2 ε$ dimensions and provide the link to the results in dimensional reduction.

The spin-dependent two-loop splitting functions

TL;DR

The paper delivers a thorough calculation of spin-dependent next-to-leading order splitting functions in QCD using the light-cone gauge, detailing how gamma5 and Levi-Civita contractions are handled across schemes. It provides complete HVBM-based results and examines alternative gamma5 prescriptions, demonstrating that suitable scheme transformations align those results with prior OPE-based findings (MVN). A clear link to dimensional reduction is established, showing how finite counterterms and mass-singularity differences map between schemes and preserve essential supersymmetric-like relations. This work enables accurate NLO QCD evolution of polarized parton densities and offers robust cross-checks for spin-dependent DIS analyses.

Abstract

We present a complete description of the calculation of the spin-dependent next-to-leading order splitting functions. The calculation is performed in the light-cone gauge. We give results for different prescriptions for the Dirac matrix in dimensions and provide the link to the results in dimensional reduction.
Paper Structure (13 sections, 52 equations, 3 figures)

This paper contains 13 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Calculation
  3. Framework
  4. NLO graphs
  5. Use of the light-cone gauge
  6. Treatment of $\gamma_5$ and $\epsilon_{\mu\nu\rho\sigma}$
  7. Results
  8. Results in the HVBM scheme
  9. Results for other $\gamma_5$ prescriptions
  10. Connection with dimensional reduction
  11. Summary
  12. Virtual Integrals
  13. Real Integrals

Figures (3)

  • Figure 1: Basic topologies of the NLO diagrams
  • Figure 2: Graphs for the $C_F T_f$ part of $\Delta P_{qg}^{(1)}$
  • Figure 3: (a) Vertex correction graph (b) One parton emission (c) Two parton emission.