Probing multi-particle unitarity with the Landau equations

TL;DR

This paper investigates the complex analytic structure of 2-to-2 scattering amplitudes for identical massive particles by analyzing Landau equations and identifying an infinite sequence of Landau curves that accumulate at finite points, revealing new insights into nonperturbative scattering.

Contribution

It systematically generates and solves Landau equations for multi-particle scattering, uncovering an infinite sequence of Landau curves and their accumulation behavior on the physical sheet.

Findings

Identified Landau curves in the multi-particle region.

Discovered an infinite sequence of Landau curves accumulating at finite points.

Provided new understanding of the analytic structure of scattering amplitudes.

Abstract

We consider the $2\to 2$ scattering amplitude of identical massive particles. We identify the Landau curves in the multi-particle region $16m^2 \leq s, t < 36m^2$. We systematically generate and select the relevant graphs and numerically solve the associated Landau equations for the leading singularity. We find an infinite sequence of Landau curves that accumulates at finite $s$ and $t$ on the physical sheet. We expect that such accumulations are generic for $s,t > 16m^2$. Our analysis sheds new light on the complicated analytic structure of nonperturbative relativistic scattering amplitudes.