Boundary Contributions of On-shell Recursion Relations With Multiple-line Deformation

TL;DR

This paper extends the analysis of boundary contributions in on-shell recursion relations to multiple-line deformations, providing a method to explicitly compute boundary terms when the amplitude's residue at infinity does not vanish.

Contribution

It generalizes the boundary behavior analysis and explicit boundary contribution calculation to cases of multiple-line deformation in on-shell recursion relations.

Findings

Boundary behaviors can be systematically extracted for multiple-line deformations.

The method enables explicit calculation of boundary contributions in complex deformations.

The approach broadens the applicability of on-shell recursion techniques.

Abstract

On-shell recursion relation has been recognized as a powerful tool for calculating tree level amplitudes in quantum field theory, but it doesn't work well when the residue of the deformed amplitude $\hat{A}(z)$ doesn't vanish at infinity of $z$. However, in such situation, we still can get the right amplitude by computing the boundary contribution explicitly. In arXiv:0801.2385, background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has also been generalized to calculate the explicit boundary operators of some amplitudes with BCFW-like deformation in arXiv:1507.00463. In this paper, we will take a step further to generalize the method into the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method.