New Soft Theorems for Two-Scalar Sigma Models

TL;DR

This paper explores soft theorems in two-scalar sigma models, revealing that Goldstone bosons exhibit Adler zero, while certain models with symmetries have unique soft behaviors without derivatives, expanding understanding of these theories.

Contribution

The paper introduces new soft theorems for two-scalar sigma models, including models with special symmetries that produce non-trivial soft behaviors without derivatives.

Findings

Goldstone bosons exhibit Adler zero with trivial soft theorems.

Certain symmetric models have soft theorems without derivatives.

Derived sum rules for classes of two-scalar sigma models.

Abstract

In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior is generically captured by the geometric soft theorem studied by Cheung et al., and the right-hand side contains derivatives of lower-point amplitudes. Inspired by the recent work on the 2D sigma models, we study one special two-scalar sigma model, where the presence of symmetries in the target space translates into a special but non-trivial soft theorem without derivatives. We further generalize the construction to two larger classes of such models and derive certain soft theorem sum rules, again avoiding the derivatives of amplitudes. Our analysis provides an interesting hierarchy of two-scalar sigma models and soft theorems, ranging from Goldstone boson case to a generic target space, and showing that there are interesting theories in between.