Addendum: Nonlinear integral equations for the sausage model

TL;DR

This paper completes the derivation of the nonlinear integral equations for the sausage model by providing a proof of a key relation, enhancing the mathematical understanding of the model.

Contribution

It offers a rigorous proof of a crucial relation in the sausage model's NLIE, strengthening the theoretical foundation of the model.

Findings

Proof of the key relation (3.24) established

Enhanced understanding of the sausage model's NLIE

Mathematical rigor added to the derivation process

Abstract

We complete the derivation of the sausage model NLIE by giving a proof of the crucial relation (3.24) of the original paper based on the analytic properties of $Q$ and $\bar Q$.