Leading order multi-soft behaviors of tree amplitudes in NLSM

TL;DR

This paper analyzes the leading order multi-soft behaviors of tree amplitudes in the nonlinear sigma model, revealing zero behaviors for odd soft pions and expressing even soft pion behaviors via Berends-Giele currents.

Contribution

It introduces a novel expression for leading soft factors in NLSM amplitudes using Berends-Giele currents, extending understanding of soft behaviors in the model.

Findings

Leading behaviors with odd soft pions are zero.

Even soft pion behaviors are expressed via products of Berends-Giele currents.

Generalization to nonadjacent soft blocks with specific soft behavior patterns.

Abstract

In this paper, we investigate multi-soft behaviors of tree amplitudes in nonlinear sigma model (NLSM). The leading behaviors of amplitudes with odd number of all-adjacent soft pions are zero. We further propose and prove that leading soft factors of amplitudes with even number all-adjacent soft pions can be expressed in terms of products of the leading order Berends-Giele sub-currents in Cayley parametrization. Each sub-current in the expression contains at most one hard pion. Discussions are generalized to amplitudes containing arbitrary number of nonadjacent soft blocks: The leading behaviors of amplitudes where at least one soft block has odd number of adjacent soft pions are zero; The leading soft factors for amplitudes where all soft blocks containing even number of soft pions are given by products of soft factors for these blocks.