Soft pion theorem, asymptotic symmetry and new memory effect

TL;DR

This paper extends the connection between soft theorems, asymptotic symmetries, and memory effects to soft pions, revealing a pion memory effect linked to spontaneously broken axial symmetry.

Contribution

It demonstrates that soft pion theorems can be formulated as Ward-Takahashi identities of the S-matrix and introduces the concept of a pion memory effect associated with asymptotic charges.

Findings

Soft pion theorem as Ward-Takahashi identity.

Identification of a pion memory effect.

Conservation of asymptotic charges related to pion dynamics.

Abstract

It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the $S$-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.