Scattering of Nambu–Goldstone Bosons

Interactions of Nambu–Goldstone bosons are constrained by spontaneously broken symmetry just like their spectrum. This chapter is devoted to one specific manifestation of interactions: scattering. This is of particular importance in subatomic physics. The discussion of scattering of Nambu–Goldstone bosons is therefore restricted to relativistic, Lorentz-invariant systems. Some references to literature dealing with a general setting also applicable to condensed-matter physics are provided. The first half of the chapter revisits the Adler zero phenomenon. A necessary and sufficient condition for a scattering amplitude to vanish in the soft limit for a single particle is derived. There is a small class of effective theories whose scattering amplitudes are softer than the naive Adler zero would suggest. It is shown how such theories can be constructed by systematically imposing specific scaling of the scattering amplitudes in the soft limit. The chapter concludes with a brief introduction to on-shell recursion methods. These allow one to reconstruct all tree-level scattering amplitudes of a theory from a finite number of seed, low-point amplitudes by utilizing a priori knowledge about the infrared behavior of the amplitudes.