Quantum Mechanics Violating Effects to Masses of Nambu-Goldstone Bosons: A Lesson for Majoron

TL;DR

This paper investigates how quantum gravity effects can induce masses in Nambu-Goldstone bosons, using the majoron as a case study, and extends theoretical formulas to include these effects.

Contribution

It introduces an extension of Dashen's formula to account for quantum gravity violating effects on pseudo Nambu-Goldstone boson masses.

Findings

Supersymmetric majoron can have a mass around keV due to dimension five potentials.

Higher-dimensional effective potentials can lead to even smaller masses.

The extended formula incorporates quantum gravity effects into mass calculations.

Abstract

We study gravitational quantum mechanics violating (QMV) effects to masses of Nambu-Goldstone bosons, taking majoron as an example. We show a supersymmetric majoron has either mass of O(keV) for the dimension five potential or smaller mass for effective potentials with higher dimensions. We extend the Dashen's formula for pseudo Nambu-Goldstone bosons to include possible effects of QMV.