The Peccei-Quinn Axion in the Next-to-Minimal Supersymmetric Standard Model

We discuss the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a Peccei-Quinn (PQ) U(1) symmetry. When this symmetry is dynamically broken by the Higgs mechanism, the resulting pseudo-Nambu-Goldstone boson takes the role of an axion. Although much of the allowed parameter space for low values of the PQ scale has been ruled out, many scenarios with a PQ scale > 10^9 GeV remain untested, allowing the NMSSM PQ axion to provide a solution to the strong CP problem and be a good dark matter candidate. Unfortunately the new particle states are so decoupled that they would not be observable at future colliders, and the NMSSM would appear indistinguishable from the minimal model. However, we show that in order to maintain vacuum stability, such a model requires that the heavy Higgs boson states have masses that lie close to approximately mu tan beta. Therefore, a measurement of the Heavy Higgs boson masses at the LHC would allow one to either rule out the NMSSM PQ axion, or provide tantalizing circumstantial evidence for its existence.