Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry

2003/11/30 by Roberto Bonciani, R. Bonciani, Pierpaolo Mastrolia +2 · 1 citation
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1016/j.nuclphysb.2004.04.011

published as Nucl.Phys. B690 (2004) 138-176 · 38 pages, 6 figures, typos corrected, version accepted by Nucl. Phys. B

arxiv created 2004/04/20 · openalex publication_date 2004/05/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q² and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Differential Equations for Two-Loop Four-Point Functions
• Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass
• Numerical evaluation of harmonic polylogarithms
• Harmonic Polylogarithms

Cited by

• Two-loop vertices in quantum field theory: infrared convergent scalar configurations
• The two loop crossed ladder vertex diagram with two massive exchanges