Tensorial Reconstruction at the Integrand Level

TL;DR

This paper introduces a new integrand-level tensorial reconstruction method for one-loop amplitude reduction, improving numerical stability and efficiency in multi-leg scattering calculations.

Contribution

The paper presents a novel tensorial reconstruction technique at the integrand level for one-loop amplitudes, enhancing stability and computational performance.

Findings

Effective handling of numerically unstable points near vanishing Gram determinants

Enables sampling with real values of the integration momentum

Optimizes reduction of complex numerator functions

Abstract

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the integration momentum. There are several interesting applications of this novel method within existing techniques for the reduction of one-loop multi-leg amplitudes: to deal with numerically unstable points, such as in the vicinity of a vanishing Gram determinant; to allow for a sampling of the numerator function based on real values of the integration momentum; to optimize the numerical reduction in the case of long expressions for the numerator functions.