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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

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.