English

Non-planar elliptic vertex

High Energy Physics - Phenomenology 2022-09-07 v2

Abstract

We consider the problem of obtaining higher order in regularization parameter ϵ\epsilon analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct integration of parametric representations in terms of iterated integrals. Taking non-planar elliptic vertex as an example we show that in addition to two mentioned methods one can use analytical solution of differential equations in terms of power series. Moreover, in the last case it is possible to obtain the exact in ϵ\epsilon results expressible either in terms of generalized hypergeometric or Kamp\'e de F\'eriet functions

Keywords

Cite

@article{arxiv.2112.05096,
  title  = {Non-planar elliptic vertex},
  author = {M. A. Bezuglov and A. I. Onishchenko},
  journal= {arXiv preprint arXiv:2112.05096},
  year   = {2022}
}

Comments

29 pages, 4 figures, representations of the obtained results in the form of hypergeometry were added

R2 v1 2026-06-24T08:11:11.282Z