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

Understand

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.