Calculating multiloop integrals using dimensional recurrence relation and D-analyticity

TL;DR

The paper reviews the DRA method for multiloop integral evaluation using dimensional recurrence relations and D-analyticity, and provides an automation-friendly derivation of the recurrences via Baikov transformation. It details both lowering and raising dimension recurrences, the role of the summing factor, and pole-structure analysis to fix constants. The approach is illustrated on a four-loop vacuum integral with four master integrals, yielding analytic expansions around D=4 and D=3 in terms of zeta-values and confirming agreement with previous work. Overall, the work demonstrates the practicality and power of the DRA method for complex multiloop calculations.

Abstract

We review the method of the calculation of multiloop integrals recently suggested in Ref.[Lee2010]. A simple method of derivation of the dimensional recurrence relation suitable for automatization is given. Some new analytic results are given.