Low Energy Theorems in N=1 Supersymmetric Theory

TL;DR

This paper explores the scattering amplitudes of Nambu-Goldstone and quasi Nambu-Goldstone bosons in N=1 supersymmetric theories, revealing their equivalence and specific vanishing properties through geometric analysis.

Contribution

It demonstrates that QNG boson scattering amplitudes match NG boson amplitudes despite arbitrary functions in the Lagrangian, highlighting geometric and symmetry aspects.

Findings

QNG boson scattering amplitudes equal NG boson amplitudes

Amplitudes with odd number of QNG bosons vanish

Scattering amplitudes are expressed by Kahler manifold curvature

Abstract

In N=1 supersymmetric theories, quasi Nambu-Goldstone (QNG) bosons appear in addition to ordinary Nambu-Goldstone (NG) bosons when the global symmetry G breaks down spontaneously. We investigate two-body scattering amplitudes of these bosons in the low-energy effective Lagrangian formalism. They are expressed by the curvature of Kahler manifold. The scattering amplitudes of QNG bosons are shown to coincide with those of NG bosons though the effective Lagrangian contains an arbitrary function, and those with odd number of QNG bosons all vanish.