General tree-level amplitudes by factorization limits

TL;DR

This paper introduces a novel method to compute tree-level amplitudes by utilizing factorization limits, providing an alternative to boundary contribution calculations in BCFW recursion, demonstrated across various theories.

Contribution

The authors propose an iterative approach to construct tree amplitudes based solely on factorization limits, bypassing the need for boundary term calculations in BCFW recursion.

Findings

Successfully applied to $4$ theory, gauge theory, Einstein-Maxwell, and Yukawa theory.

Constructed amplitudes that match physical pole factorization limits.

Method cannot determine full amplitudes when polynomials are present.

Abstract

To find boundary contributions is a rather difficult problem when applying the BCFW recursion relation. In this paper, we propose an approach to bypass this problem by calculating general tree amplitudes that contain no polynomial using factorization limits. More explicitly, we construct an expression iteratively, which produces correct factorization limits for all physical poles, and does not contain other poles, then it should be the correct amplitude. To some extent, this approach can be considered as an alternative way to find boundary contributions. To demonstrate our approach, we present several examples: $\phi^4$ theory, pure gauge theory, Einstein-Maxwell theory, and Yukawa theory. While the amplitude allows the existence of polynomials which satisfy correct mass dimension and helicities, this approach is not applicable to determine the full amplitude.