Constructing tree amplitudes of scalar EFT from double soft theorem

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. In this paper we propose a novel method based on exploiting the double soft theorem for scalars, which can be applied to a wider range. 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.