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arXiv · 2510.09403

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

J. Ablinger·J. Blümlein·A. De Freitas·A. von Manteuffel·C. Schneider·K. Schönwald
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Abstract

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

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J. Ablinger, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schönwald. 2025-10-10. The two-mass contributions to the three-loop massive operator matrix elements $\tilde{A}_{Qg}^{(3)}$ and $\Delta \tilde{A}_{Qg}^{(3)}$. https://arxiv.org/abs/2510.09403

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