The origin of the mass of the Nambu-Goldstone bosons

TL;DR

This paper explores how chemical potentials that explicitly break symmetry can give mass to Nambu-Goldstone bosons, revealing conditions under which they can merge into a single degree of freedom with an effective mass.

Contribution

It introduces a novel method based on interaction histories and triangle relations to explain the mass generation of Nambu-Goldstone bosons under explicit symmetry breaking.

Findings

Mass of Nambu-Goldstone bosons can arise from explicit symmetry breaking by chemical potential.

Pairs of massive Nambu-Goldstone bosons can combine into a single effective degree of freedom.

Discussion of possible mass oscillations for Nambu-Goldstone bosons.

Abstract

We explain the origin of the mass for the Nambu-Goldstone bosons when there is a chemical potential in the action which breaks explicitly the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu-Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu-Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu-Goldstone bosons are discussed.