Extended projection method for massive fermions * * Supported by the National Natural Science Foundation of China (11675185)

Yefan Wang,Zhao Li

doi:10.1088/1674-1137/44/3/033102

Abstract

Tensor reduction is of considerable importance in calculations of multi-loop amplitudes, and the projection method is one of the most popular approaches for tensor reduction. However, the projection method can be problematic when applied to amplitudes with massive fermions, due to the inconsistency between helicity and chirality. We propose an extended projection method for reducing the loop amplitude which contains a fermion chain with two massive spinors. The extension is achieved by decomposing one of the massive spinors into two massless spinors, the “null spinor” and the “reference spinor”. The extended projection method can be effectively applied in all processes, including the production of massive fermions. We present the tensor reduction for a virtual Z boson decaying into a top-quark pair as a demonstration of our approach.

Highlights

After the discovery of the Higgs boson, the continuous improvement of experiment accuracy at the CERN Large Hadron Collider (LHC) demands the precise theoretical predictions to high order corrections
In this paper, based on the massive spinor decomposition [56–58], we propose to extend the projection method to reduce the loop amplitude for any process including production of massive fermions
In this paper, based on the massive spinor decomposition, we proposed an extended projection method to reduce the loop amplitude containing fermion chain with two massive spinors

Summary

Introduction

After the discovery of the Higgs boson, the continuous improvement of experiment accuracy at the CERN Large Hadron Collider (LHC) demands the precise theoretical predictions to high order corrections. For the one-loop amplitude, a variety of reduction methods has been developed in the past decades [1,2,3,4,5,6,7,8,9,10]. Some complicated processes, e.g. e+e− → Z⋆ → tt, can confront serious problem during tensor reduction. Many important researches have been done by using projection method, such as high order QCD corrections to the Higgs production [50–53] and vector boson production [54, 55]. In this paper, based on the massive spinor decomposition [56–58], we propose to extend the projection method to reduce the loop amplitude for any process including production of massive fermions.

Standard Projection method

Projection method for massive fermion chain

One-loop Example

Two-loop Example t

D2D3D4

Conclusion