Massive 3-loop ladder diagrams for quarkonic local operator matrix elements. (English) Zbl 1262.81184
Summary: 3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with \(\xi \in \{1,1/2,2\}\) emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region \(Q^{2}\gg m^{2}\).
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T18 | Feynman diagrams |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 33C65 | Appell, Horn and Lauricella functions |
| 81U35 | Inelastic and multichannel quantum scattering |
| 81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
Software:
HarmonicSumsReferences:
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