A new approach for amplitudes with multiple fermion lines

TL;DR

This paper introduces a novel recursive method for simplifying tree-level amplitudes with multiple fermion lines, significantly improving computational efficiency and performance over existing packages.

Contribution

It presents a new recursive approach that reduces fermion line calculations to two vectors, enhancing speed and simplicity in amplitude computations.

Findings

FDC package outperforms other tools in multi-fermion processes

The new method achieves high efficiency in pure amplitude square calculations

Comparable or better performance than WHIZARD in specific amplitude computations

Abstract

A new approach for tree-level amplitudes with multiple fermion lines is presented. It mainly focuses on the simplification of fermion lines. By calculating two vectors recursively without any matrix multiplications, the result of a fermion line is reduced to a very compact form depending only on the two vectors. The comparisons with other packages are presented, and the results show that our package FDC gives a very good performance in the processes of multiple fermion lines with this new approach and some other improvements. A further comparison with WHIZARD shows that this new approach has a competitive efficiency in computing pure amplitude square without phase space integration.