The R Axion From Dynamical Supersymmetry Breaking

TL;DR

The paper analyzes the $R$-axion in generic dynamical SUSY-breaking theories, showing that explicit $R$-symmetry breaking by a constant superpotential term $W_0$—needed to tune the cosmological constant—generates a mass for the axion. It develops a general mass formula and analyzes three model classes, providing an explicit calculation in the 3-2 renormalizable hidden-sector model, including supergravity couplings. The results indicate that visible-sector models typically evade astrophysical bounds due to a heavy enough axion, NRHS models face cosmological challenges from electroweak-scale axions, and RHS models yield very heavy axions ($\\\sim 10^7$ GeV) that can nonetheless produce gravitinos after inflation, constraining the reheat temperature in a way that can be competitive with or stronger than thermal gravitino bounds. The study demonstrates that the presence of an $R$-axion does not by itself rule out dynamical SUSY-breaking constructions; cosmological constraints depend sensitively on the model class and early-universe history, particularly reheating.

Abstract

All generic, calculable models of dynamical supersymmetry breaking have a spontaneously broken $R$ symmetry and therefore contain an $R$ axion. We show that the axion is massive in any model in which the cosmological constant is fine-tuned to zero through an explicit $R$-symmetry-breaking constant. In visible-sector models, the axion mass is in the 100 MeV range and thus evades astrophysical bounds. In nonrenormalizable hidden-sector models, the mass is of order of the weak scale and can have dangerous cosmological consequences similar to those already present from other fields. In renormalizable hidden- sector models, the axion mass is generally quite large, of order $10^7$ GeV. Typically, these axions are cosmologically safe. However, if the dominant decay mode is to gravitinos, the potentially large gravitino abundance that arises from axion decay after inflation might affect the successful predictions of big-bang nucleosynthesis. We show that the upper bound on the reheat temperature after standard inflation can be competitive with or stronger than bounds from thermal gravitino production, depending on the model and the gravitino mass.