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<p>We calculate the two-mass three-loop contributions to the unpolarized and polarized massive operator matrix elements <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\widetilde{A}}_{Qg}^{(3)}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\Delta \widetilde{A}}_{Qg}^{(3)}\)</EquationSource> </InlineEquation> in <i>x</i>-space for a general mass ratio by using a semi-analytic approach. We also compute Mellin moments up to <i>N</i> = 2000(3000) by an independent method, to which we compare the results in <i>x</i>-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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(O({T}_{F}^{2})\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(O({T}_{F}^{3})\)</EquationSource> </InlineEquation> terms contributing to the operator matrix elements. The present result completes the calculation of all unpolarized and polarized massive three-loop operator matrix elements.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月16日

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  • J. Ablinger,
  • J. Blümlein,
  • A. De Freitas,
  • A. von Manteuffel,
  • C. Schneider,
  • K. Schönwald

摘要

We calculate the two-mass three-loop contributions to the unpolarized and polarized massive operator matrix elements \({\widetilde{A}}_{Qg}^{(3)}\) and \({\Delta \widetilde{A}}_{Qg}^{(3)}\) 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 \(O({T}_{F}^{2})\) and \(O({T}_{F}^{3})\) terms contributing to the operator matrix elements. The present result completes the calculation of all unpolarized and polarized massive three-loop operator matrix elements.