Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals

TL;DR

The paper presents a method to explicitly find meromorphic solutions to higher-order recurrence relations, enhancing the DRA method for multiloop integral calculations by clarifying solution properties.

Contribution

It introduces a recursive pole-sum approach for solving recurrence relations, improving the analytical understanding needed for multiloop integral computations.

Findings

Explicit solutions for recurrence relations with known pole structures

Clear determination of solution behavior at infinity

Application to multicomponent master integrals using DRA method

Abstract

We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given. The main advantage of the described approach is that the analytical properties of the solutions are very clear (the position of poles is explicit, the behavior at infinity can be easily determined). These are exactly the properties that are required for the application of the multiloop calculation method based on dimensional recurrence relations and analyticity (the DRA method).