English

Three-loop vertex integrals at symmetric point

High Energy Physics - Phenomenology 2021-06-17 v1 High Energy Physics - Theory

Abstract

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε\varepsilon-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

Keywords

Cite

@article{arxiv.2104.06958,
  title  = {Three-loop vertex integrals at symmetric point},
  author = {Andrey Pikelner},
  journal= {arXiv preprint arXiv:2104.06958},
  year   = {2021}
}

Comments

14 pages, many figures

R2 v1 2026-06-24T01:10:10.437Z