Scattering amplitudes of massive Nambu-Goldstone bosons

TL;DR

This paper demonstrates that massive Nambu-Goldstone bosons, despite having a gap, have scattering amplitudes that vanish in the long-wavelength limit due to symmetry protection, similar to gapless NG bosons.

Contribution

It reveals that symmetry protects the scattering amplitudes of massive Nambu-Goldstone bosons, extending the understanding of their behavior beyond the gapless case.

Findings

Scattering amplitudes of mNG bosons vanish in the long-wavelength limit.

No kinematic singularities occur in processes involving soft mNG bosons.

Symmetry protection applies to both gapless and massive NG bosons.

Abstract

Massive Nambu-Goldstone (mNG) bosons are quasiparticles whose gap is determined exactly by symmetry. They appear whenever a symmetry is broken spontaneously in the ground state of a quantum many-body system, and at the same time explicitly by the system's chemical potential. In this paper, we revisit mNG bosons and show that apart from their gap, symmetry also protects their scattering amplitudes. Just like for ordinary gapless NG bosons, the scattering amplitudes of mNG bosons vanish in the long-wavelength limit. Unlike for gapless NG bosons, this statement holds for any scattering process involving one or more external mNG states; there are no kinematic singularities associated with the radiation of a soft mNG boson from an on-shell initial or final state.