English

The two-mass contributions to the three-loop massive operator matrix elements $\tilde{A}_{Qg}^{(3)}$ and $\Delta \tilde{A}_{Qg}^{(3)}$

High Energy Physics - Phenomenology 2025-10-13 v1 High Energy Physics - Theory

Abstract

We calculate the two-mass three-loop contributions to the unpolarized and polarized massive operator matrix elements A~Qg(3)\tilde{A}_{Qg}^{(3)} and ΔA~Qg(3)\Delta \tilde{A}_{Qg}^{(3)} in xx-space for a general mass ratio by using a semi-analytic approach. We also compute Mellin moments up to N=2000(3000)N = 2000 (3000) by an independent method, to which we compare the results in xx-space. In the polarized case, we work in the Larin scheme. We present numerical results. The two-mass contributions amount to about 50%50 \% of the full \textcolor{blue}{O(TF2)O(T_F^2)} and \textcolor{blue}{O(TF3)O(T_F^3)} terms contributing to the operator matrix elements. The present result completes the calculation of all unpolarized and polarized massive three-loop operator matrix elements.

Keywords

Cite

@article{arxiv.2510.09403,
  title  = {The two-mass contributions to the three-loop massive operator matrix elements $\tilde{A}_{Qg}^{(3)}$ and $\Delta \tilde{A}_{Qg}^{(3)}$},
  author = {J. Ablinger and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schönwald},
  journal= {arXiv preprint arXiv:2510.09403},
  year   = {2025}
}

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50 pages Latex