Determining the closed forms of the anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

DOI10.1016/j.cpc.2009.06.020zbMath1197.81037arXiv0902.4091OpenAlexW2007057571MaRDI QIDQ711793

Carsten Schneider, Manuel Kauers, Johannes Blümlein, Sebastian Klein

Publication date: 28 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4091

zbMATH Keywords

difference equationsharmonic sumsadvanced computer algebracalculation of 3-loop single scale quantitiesproduct-and-sum fields

Mathematics Subject Classification ID

Related Items (31)

The two-loop massless off-shell QCD operator matrix elements to finite terms ⋮ Analytic computing methods for precision calculations in quantum field theory ⋮ Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses ⋮ Iterated binomial sums and their associated iterated integrals ⋮ The method of arbitrarily large moments to calculate single scale processes in quantum field theory ⋮ The three-loop splitting functions \(P_{q g}^{(2)}\) and \(P_{g g}^{(2, \operatorname{N}_{\operatorname{F}})}\) ⋮ The multiple zeta value data mine ⋮ The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements ⋮ The heavy fermion contributions to the massive three loop form factors ⋮ Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱ ⋮ The 3-loop pure singlet heavy flavor contributions to the structure function \(F_2(x, Q^2)\) and the anomalous dimension ⋮ The first-order factorizable contributions to the three-loop massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\) ⋮ The massless three-loop Wilson coefficients for the deep-inelastic structure functions \(F_2\), \(F_L\), \(xF_3\) and \(g_1\) ⋮ The inverse Mellin transform via analytic continuation ⋮ The \(O(\alpha_s^3)\) massive operator matrix elements of \(O(n_f)\) for the structure function \(F_{2}(x,Q^{2})\) and transversity ⋮ A symbolic summation approach to Feynman integral calculus ⋮ Massive 3-loop ladder diagrams for quarkonic local operator matrix elements ⋮ Three-loop anomalous dimension of the non-singlet transversity operator in QCD ⋮ The \(O({\alpha}_s^2)\) heavy quark corrections to charged current deep-inelastic scattering at large virtualities ⋮ The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements ⋮ Large-\(n_{f}\) contributions to the four-loop splitting functions in QCD ⋮ Structural theorems for symbolic summation ⋮ THE QCD COUPLING AND PARTON DISTRIBUTIONS AT HIGH PRECISION ⋮ Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms ⋮ Large Scale Analytic Calculations in Quantum Field Theories ⋮ Simplifying Multiple Sums in Difference Fields ⋮ The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements ⋮ Analytic Integration Methods in Quantum Field Theory: An Introduction ⋮ Extensions of the AZ-Algorithm and the Package MultiIntegrate ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• gfun
• SIGMA
• Mincer
• FORM
• HarmonicSums
• GeneratingFunctions

Cites Work

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