An Explicit Expression of Generating Function for One-Loop Tensor Reduction

TL;DR

This paper derives an explicit formula for the generating function used in reducing one-loop tensor integrals, utilizing a recursive relation based on Feynman parametrization and a differential equation, revealing insights into loop amplitude structures.

Contribution

It presents a novel explicit expression for the generating function of one-loop tensor reduction, derived through a recursive relation and differential equation approach.

Findings

Provides an explicit generating function expression for tensor reduction.

Reveals the complex analytic structure of loop amplitudes.

Introduces a recursive relation based on Feynman parametrization.

Abstract

This work introduces an explicit expression for the generation function for the reduction of an $n$-gon to an $(n-k)$-gon. A novel recursive relation of generation function is formulated based on Feynman Parametrization in projective space, involving a single ordinary differential equation. The explicit formulation of generation functions provides crucial insights into the complex analytic structure inherent in loop amplitudes.