Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D

TL;DR

This paper introduces a method leveraging dimensional recurrence relations and complex analysis to derive rapidly converging analytical representations of loop integrals in quantum field theory.

Contribution

It presents a novel approach using complex variable techniques and recurrence relations to compute loop integrals more efficiently.

Findings

Derived exponentially converging sum representations of loop integrals.

Applied the method to multiple examples demonstrating effectiveness.

Provided a regular framework for analytical loop integral calculations.

Abstract

We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop integrals. The representations derived have a form of exponentially converging sums. Several examples of the developed technique are given.