The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory

Abstract

We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman integrals of loop corrections to physical quantities. These scalar quantities have a much simpler mathematical structure than the complete quantity. A sufficiently large set of moments may even allow the analytic reconstruction of the whole quantity considered, holding in case of first order factorizing systems. In any case, one may derive highly precise numerical representations in general using this method, which is otherwise completely analytic.

4 pages LATEX

References in corpus (8)

• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• A Refined Difference Field Theory for Symbolic Summation
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Iterated Binomial Sums and their Associated Iterated Integrals
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• First Forcer results on deep-inelastic scattering and related quantities

Cited by in corpus (23)

• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• Massive vector form factors to three loops
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• NNLO QCD$\times$EW corrections to Z production in the $q\bar{q}$ channel
• The two-mass contribution to the three-loop pure singlet operator matrix element
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• The three-loop polarized pure singlet operator matrix element with two different masses
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• NNLO mixed EW-QCD corrections to single vector boson production
• Singlet and non-singlet three-loop massive form factors
• Three loop QCD corrections to heavy quark form factors