The \(O(\alpha_s^3 T_F^2)\) contributions to the gluonic operator matrix element. (English) Zbl 1323.81126
Summary: The \(O(\alpha_s^3 T_F^2 C_F(C_A))\) contributions to the transition matrix element \(A_{g g, Q}\) 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.
MSC:
| 81V35 | Nuclear physics |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
| 11G55 | Polylogarithms and relations with \(K\)-theory |
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