Multi-leg one-loop massive amplitudes from integrand reduction via Laurent expansion

Hans Van Deurzen,Tiziano Peraro,Edoardo Mirabella,Pierpaolo Mastrolia,Giovanni Ossola,Gionata Luisoni

doi:10.1007/jhep03(2014)115

Abstract

We present the application of a novel reduction technique for one-loop scattering amplitudes based on the combination of the integrand reduction and Laurent expansion. We describe the general features of its implementation in the computer code Ninja, and its interface to GoSam. We apply the new reduction to a series of selected processes involving massive particles, from six to eight legs.

Highlights

Scattering amplitudes in quantum field theories are analytic functions of the kinematic variables of the interacting particles, they can be determined by studying the structure of their singularities.The multi-particle factorization properties of the amplitudes become transparent when internal particles go on their mass-shell [1, 2]
We present the application of a novel reduction technique for one-loop scattering amplitudes based on the combination of the integrand reduction and Laurent expansion
Significant improvements were achieved with the d-dimensional extension of integrandreduction methods [73,74,75], which expose a richer polynomial structure of the integrand and allows for the combined determination of both cut-constructible and rational terms at once. This idea of performing unitarity-cuts in d-dimension was the basis for the development of Samurai, which extends the OPP polynomial structures to include an explicit dependence on the (d − 4)-dimensional parameter needed for the automated computation of the full rational term

Summary

Introduction

Scattering amplitudes in quantum field theories are analytic functions of the kinematic variables of the interacting particles, they can be determined by studying the structure of their singularities. Significant improvements were achieved with the d-dimensional extension of integrandreduction methods [73,74,75], which expose a richer polynomial structure of the integrand and allows for the combined determination of both cut-constructible and rational terms at once This idea of performing unitarity-cuts in d-dimension was the basis for the development of Samurai, which extends the OPP polynomial structures to include an explicit dependence on the (d − 4)-dimensional parameter needed for the automated computation of the full rational term. It includes the parametrization of the residue of the quintuplecut [76] and implements the numerical sampling via Discrete Fourier Transform [64].

Integrand and integral decomposition

Scattering amplitudes via Laurent expansion

Interfacing Ninja with GoSam

Precision tests

Applications to massive amplitudes

Conclusions