Interplay between the loop-tree duality and helicity amplitudes

G. F. R. Sborlini,F. Driencourt-Mangin,G. Rodrigo,W. J. Torres Bobadilla

doi:10.1103/physrevd.105.016012

G. F. R. Sborlini, F. Driencourt-Mangin + Show 2 more

Open Access

https://doi.org/10.1103/physrevd.105.016012

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Abstract

The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop-tree duality (LTD) representation of multiloop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyze illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalization of IR and UV finite helicity amplitudes and present a fully automated numerical implementation that provides efficient expressions, which are integrable directly in four space-time dimensions.

Highlights

In order to unveil the fundamental components of matter and their interactions, it is necessary to analyze highlyprecise experimental data obtained from colliders using accurate theoretical predictions
We explore the computational advantages of the loop-tree duality (LTD)-based representation combined with the spinor-helicity formalism, which constitutes the central part of this paper
We have presented an efficient numerical implementation of helicity amplitudes in the LTD representation

Summary

INTRODUCTION

In order to unveil the fundamental components of matter and their interactions, it is necessary to analyze highlyprecise experimental data obtained from colliders using accurate theoretical predictions. With the purpose of achieving a higher accuracy in the theoretical predictions, it is mandatory to explore higher perturbative orders and compute multiloop amplitudes with high multiplicity To tackle these calculations, several methods have been developed in the last years. We use the momentum twistors’ variables [27] to implement simplifications in the integrand of the helicity amplitudes These variables, due to their mathematical properties, allow us to express any kinematic process in terms of the minimal set of variables. We make use of the computational tools developed throughout this paper This allows us to support the feasibility of the LTD-based numerical strategy with realistic scattering processes, as well as its efficiency.

LOOP-TREE DUALITY IN A NUTSHELL

Multiple poles and IBPs

GENERATION OF THE KINEMATICS

Parametrization of the loop momentum

LOCAL UV RENORMALIZATION

APPLICATIONS AT ONE LOOP

Dν11 Dν22 Dν33 Dν44 Dν55 Dν66 Dν77

CONCLUSIONS AND FUTURE DIRECTIONS

Little group scaling

Momentum twistor variables