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The O(α_s³ T_F²) Contributions to the Gluonic Operator Matrix Element

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arxiv 1405.4259 v1 pith:BG675XFQ submitted 2014-05-16 hep-ph hep-th

The O(α_s³ T_F²) Contributions to the Gluonic Operator Matrix Element

J. Ablinger , J. Bl\"umlein , A. De Freitas , A. Hasselhuhn , A. von Manteuffel , M. Round , C. Schneider This is my paper
classification hep-ph hep-th
keywords alphacontributionselementgraphsharmoniclinesmassivematrix
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The $O(\alpha_s^3 T_F^2 C_F (C_A))$ contributions to the transition matrix element $A_{gg,Q}$ relevant for the variable flavor number scheme at 3--loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In $x$-space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines.

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