On single and double soft behaviors in NLSM

TL;DR

This paper investigates the single and double soft limits of tree-level currents and amplitudes in the nonlinear sigma model, revealing new leading and sub-leading behaviors and their relations via KK identities.

Contribution

It introduces and proves the leading soft behavior of off-shell currents with a single soft particle and analyzes double soft behaviors, including nonadjacent cases, in NLSM.

Findings

Proved the leading soft behavior of single soft currents.

Established leading and sub-leading double soft behaviors for adjacent particles.

Derived soft behaviors for nonadjacent particles using KK relations.

Abstract

In this paper, we study the single and double soft behaviors of tree level off-shell currents and on-shell amplitudes in nonlinear sigma model(NLSM). We first propose and prove the leading soft behavior of the tree level currents with a single soft particle. In the on-shell limit, this single soft emission becomes the Adler's zero. Then we establish the leading and sub-leading soft behaviors of tree level currents with two adjacent soft particles. With a careful analysis of the on-shell limit, we obtain the double soft behaviors of on-shell amplitudes where the two soft particles are adjacent to each other. By applying Kleiss-Kuijf (KK) relation, we further obtain the leading and sub-leading behaviors of amplitudes with two nonadjacent soft particles.