On Multi-step BCFW Recursion Relations

TL;DR

This paper introduces and analyzes the multi-step BCFW recursion relations, a new algorithm for calculating scattering amplitudes that systematically completes calculations without relying on specific field theory knowledge.

Contribution

It presents a systematic method for amplitude calculation using multi-step BCFW recursion, revealing mathematical properties and applying it to the Standard Model plus gravity.

Findings

The algorithm completes amplitude calculations in finite steps.

It identifies terms that cannot be determined by the method.

Application to Standard Model plus gravity demonstrates its effectiveness.

Abstract

In this paper, we extensively investigate the new algorithm known as the multi-step BCFW recursion relations. Many interesting mathematical properties are found and understanding these aspects, one can find a systematic way to complete the calculation of amplitude after finite, definite steps and get the correct answer, without recourse to any specific knowledge from field theories, besides mass dimension and helicities. This process consists of the pole concentration and inconsistency elimination. Terms that survive inconsistency elimination cannot be determined by the new algorithm. They include polynomials and their generalizations, which turn out to be useful objects to be explored. Afterwards, we apply it to the Standard Model plus gravity to illustrate its power and limitation. Ensuring its workability, we also tentatively discuss how to improve its efficiency by reducing the steps.