Extended Projection Method for Massive Fermion

TL;DR

This paper introduces an extended projection method for tensor reduction in multi-loop amplitudes involving massive fermions, overcoming previous limitations related to helicity and chirality inconsistencies.

Contribution

The authors develop a novel extension of the projection method by decomposing massive spinors into massless components, enabling tensor reduction for processes with massive fermions.

Findings

Successfully applied to Z boson decay to top-quark pairs

Addresses helicity-chirality inconsistency in tensor reduction

Enhances computational techniques for multi-loop amplitude calculations

Abstract

Tensor reduction is important for multi-loop amplitude calculation. And the projection method is one of the most popular approaches for tensor reduction. However, projection method could be problematic for amplitude with massive fermions due to the inconsistency between helicity and chirality. We propose an approach to extend the projection method to reduce the loop amplitude containing fermion chain with two massive spinors. The extension is achieved by decomposing one of the massive spinors into two specific massless spinors, "null spinor" and "reference spinor". Then the extended projection method can be safely implemented for all the processes including the production of massive fermions. Finally we present the tensor reduction for the virtual Z boson decaying to top-quark pair to demonstrate our approach.