2009

Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

Blümlein, J., Kauers, M., Klein, S. et al.

Understand

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space.

It is often easier to calculate fixed moments for these quantities compared to a direct attempt to derive them in terms of harmonic sums and their generalizations involving the Mellin parameter $N$.
Starting from a sufficiently large number of given moments, we establish linear recurrence relations of lowest possible order with polynomial coefficients of usually high degree.
Then these recurrence equations are solved in terms of d'Alembertian solutions where the involved nested sums are represented in optimal nested depth.

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