Amplitude Zeroes in Collinear Processes or What Is Left from a Factorizable 2d Model in Higher Dimensions

TL;DR

This paper demonstrates that in the 2+1 dimensional Thirring model, the S-matrix factorizes for collinear processes, leading to the nullification of all higher multiplicity amplitudes beyond two, revealing residual effects of a 2D factorization in higher dimensions.

Contribution

It shows that the tree-level S-matrix in the 2+1D Thirring model factorizes for collinear processes, nullifying all multi-particle amplitudes beyond two.

Findings

S-matrix factorizes for collinear processes in 2+1D Thirring model

Nullification of all collinear 2→n amplitudes for n > 2

Residual effects of 2D factorization in higher dimensions

Abstract

We show that for collinear processes, i.e. processes where the incoming and outgoing momenta are aligned along the same line, the S-matrix of the tree level 2+1 dimensional Thirring model factorizes: any S - matrix element is a product of $2\rightarrow 2$ elements. In particular this means nullification of all collinear $2 \rightarrow n$ amplitudes for $n > 2$.