Tensor Loop Reduction via the Baikov Representation and an Auxiliary Vector

TL;DR

This paper presents a novel, efficient method for reducing one-loop integrals by using an auxiliary vector and the Baikov representation, enabling systematic solutions for complex tensor and pole structures.

Contribution

It introduces a new reduction technique employing an auxiliary vector and Baikov representation, simplifying the process of one-loop integral reduction with recursive IBP relations.

Findings

Effective reduction of tensor and higher pole integrals

Recursive IBP relations enable systematic solutions

Applicable to degenerate cases in one-loop calculations

Abstract

In this paper, we introduce a simple and efficient approach for the general reduction of one-loop integrals. Our method employs the introduction of an auxiliary vector and the identification of the tensor structure as an auxiliary propagator. This key insight allows us to express a wide range of one-loop integrals, encompassing both tensor structures and higher poles, in the Baikov representation. By establishing an integral-by-parts (IBP) relation, we derive a recursive formula that systematically solves the one-loop reduction problem, even in the presence of various degenerate cases. Our proposed strategy is characterized by its simplicity and effectiveness, offering a significant advancement in the field of one-loop calculations.