The Loop-by-Loop Baikov Representation -- Strategies and Implementation

TL;DR

This paper explores the loop-by-loop Baikov representation for Feynman integrals, proposing an optimal parametrization strategy and providing a Mathematica implementation to facilitate its use.

Contribution

It introduces a detailed strategy for optimal parametrization in the loop-by-loop Baikov representation and provides a new Mathematica package for its computation.

Findings

Optimal parametrization reduces the number of variables.

The BaikovPackage enables efficient generation of Baikov representations.

Discussion of subtleties and open problems in Baikov representations.

Abstract

In this paper, we discuss the Baikov representation of Feynman integrals in its standard and loop-by-loop variants. The Baikov representation is a parametric representation, which has as its defining feature the fact that the integration variables are the propagators of the Feynman integral. For the loop-by-loop Baikov representation, we discuss in detail a strategy for how to make an optimal parametrization which is one that minimizes the number of extra integration variables that have to be introduced for a given Feynman integral. Furthermore, we present a Mathematica implementation, named BaikovPackage, that is able to generate the Baikov representation in its standard and loop-by-loop varieties. We also discuss some subtleties and open problems regarding Baikov representations.