Direct reduction of multiloop multiscale scattering amplitudes

Yefan Wang,Najam Ul Basat,Zhao Li

doi:10.1103/physrevd.101.076023

Abstract

We propose an alternative approach based on series representation to directly reduce multi-loop multi-scale scattering amplitude into set of freely chosen master integrals. And this approach avoid complicated calculations of inverse matrix and dimension shift for tensor reduction calculation. During this procedure we further utilize the Feynman parameterization to calculate the coefficients of series representation and obtain the form factors. Conventional methodologies are used only for scalar vacuum bubble integrals to finalize the result in series representation form. Finally, we elaborate our approach by presenting the reduction of a typical two-loop amplitude for W boson production.

Highlights

The CERN Large Hadron Collider (LHC) is the most accurate experiment on the elementary particle physics at present, and the generation lepton colliders have been proposed aiming at higher accuracy
The Passarino-Veltman reduction algorithm [2,3,4,5] has been widely used in enormous number of investigations on the next-to-leading order (NLO) effects for the Standard Model (SM) processes and some new physics processes
In this paper, based on the series representation [59,60], we propose an alternative reduction approach that can directly reduce loop amplitude to master integrals so that the complexity of tensor reduction and integration by part (IBP) reduction can be relieved

Summary

INTRODUCTION

The CERN Large Hadron Collider (LHC) is the most accurate experiment on the elementary particle physics at present, and the generation lepton colliders have been proposed aiming at higher accuracy. For some complicated scattering processes, e.g., the full nextto-next-to-leading order QCD correction to single-top production [36], the project matrix could become so big that its inversion may seriously challenge the computation resource Another approach for tensor reduction is Tarasov’s method [37] based on Schwinger parametrization 38,39]]. After the successful tensor reduction the loop amplitude becomes linear combination of scalar integrals, whose number could be order Oð104Þ for complicated processes. To efficiently evaluate the multiscale multiloop amplitude one better keep the freedom to choose master integrals This can be achieved by series representation [59], which can be used to solve the tensor reduction as we will show in the following.

AMPLITUDE REDUCTION

EXAMPLE

CONCLUSIONS