Constructing tree amplitudes of scalar EFT from double soft theorem

TL;DR

This paper introduces a novel method using double soft theorems to construct scalar EFT tree amplitudes, extending beyond the Adler zero approach, and demonstrates its effectiveness on NLSM and related models.

Contribution

It proposes a new soft theorem-based technique for constructing scalar EFT amplitudes, including higher-derivative corrections, with minimal initial assumptions.

Findings

Successfully constructed NLSM tree amplitudes using the method.

Extended the construction to pion amplitudes with higher-derivative interactions.

Formulated all amplitudes as universal expansions in an appropriate basis.

Abstract

The well known Adler zero can fully determine tree amplitudes of non-linear sigma model (NLSM), but fails to fix tree pion amplitudes with higher-derivative interactions. To fill this gap, in this paper we propose a new method based on exploiting the double soft theorem for scalars, which can be applied to a wider range. A remarkable feature of this method is, we only assume the universality of soft behavior at the beginning, and determine the explicit form of double soft factor in the process of constructing amplitudes. To test the applicability, we use this method to construct tree NLSM amplitudes and tree amplitudes those pions in NLSM couple to bi-adjoint scalars. We also construct the simplest pion amplitudes which receive leading higher-derivative correction, with arbitrary number of external legs. All resulted amplitudes are formulated as universal expansions to appropriate basis.