English

The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$

High Energy Physics - Phenomenology 2018-05-09 v1 High Energy Physics - Experiment High Energy Physics - Theory

Abstract

We calculate the two-mass QCD contributions to the massive operator matrix element Agg,QA_{gg,Q} at O(αs3)\mathcal{O} (\alpha_s^3) in analytic form in Mellin NN- and zz-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin NN-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to zz-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.

Keywords

Cite

@article{arxiv.1804.02226,
  title  = {The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$},
  author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
  journal= {arXiv preprint arXiv:1804.02226},
  year   = {2018}
}

Comments

99 pages LATEX, 2 Figures

R2 v1 2026-06-23T01:15:57.665Z