A new reduction strategy for special negative sectors of planar two-loop integrals without Laporta algorithm

TL;DR

This paper introduces a novel, faster reduction method for specific sectors of planar two-loop integrals with negative indices, utilizing the Baikov representation, bypassing the traditional Laporta algorithm.

Contribution

The authors develop an alternative, efficient reduction strategy for negative sectors of planar two-loop integrals using Baikov representation, avoiding the Laporta algorithm.

Findings

The new method is significantly faster than traditional approaches.

It effectively reduces integrals without relying on the Laporta algorithm.

The approach is applicable to sectors where the index is negative.

Abstract

In planar two-loop integrals there is a dedicated sector such that when its index is zero, the two-loop integral decomposes into the product of two one-loop integrals. We show an alternative reduction strategy for these sectors when their index is negative using the Baikov representation. This reduction strategy is free from the Laporta algorithm. It follows a top-down approach and is much faster than approaches based on the brute-force, conventional integration by parts identities.