# On the massless tree-level S-matrix in 2d sigma models

## TL;DR

This paper investigates the properties of massless tree-level S-matrices in 2d sigma models, revealing that unlike massive cases, they do not exhibit integrability features such as factorization and particle production is observed even in integrable models.

## Contribution

It demonstrates that massless tree-level S-matrices in 2d sigma models lack the integrability-linked factorization seen in massive cases and explores IR ambiguities and T-duality effects.

## Key findings

- Massless S-matrices fail to factorize in integrable models.
- Particle production occurs in several integrable 2d models.
- IR ambiguities can cause anomalies in S-matrix equivalence.

## Abstract

Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d sigma models expanded near the trivial vacuum. We find that, in contrast to the standard massive case, there is no apparent link between massless S-matrices and integrability: in well-known integrable models the tree-level massless S-matrix fails to factorize and exhibits particle production. Such tree-level particle production is found in several classically integrable models: the principal chiral model, its classically equivalent "pseudo-dual" model, its non-abelian dual model and also the SO(N+1)/SO(N) coset model. The connection to integrability may, in principle, be restored if one expands near a non-trivial vacuum with massive excitations. We discuss IR ambiguities in 2d massless tree-level amplitudes and their resolution using either a small mass parameter or the i epsilon-regularization. In general, these ambiguities can lead to anomalies in the equivalence of the S-matrix under field redefinitions, and may be linked to the observed particle production in integrable models. We also comment on the transformation of massless S-matrices under sigma model T-duality, comparing the standard and the "doubled" formulations (with T-duality covariance built into the latter).