Some necessary conditions for allowing the PQ scale as high as M_{GUT} in SUSY models with an axino or neutralino LSP

TL;DR

This paper explores conditions under which the Peccei-Quinn scale can reach the GUT scale in SUSY models with axino or neutralino LSP, addressing overabundance issues via entropy injection and relic density constraints.

Contribution

It demonstrates that large entropy injection from saxion decays can allow high PQ scales in SUSY models, relaxing previous constraints and providing new viable parameter space.

Findings

High PQ scale (up to M_{GUT}) is possible with saxion decay-induced entropy injection.

Relic density and BBN constraints can be satisfied with specific saxion mass and initial conditions.

Allowed reheat temperature depends on the LSP type, with higher T_R feasible for neutralino LSP.

Abstract

We examine some conditions which are needed to allow the Peccei-Quinn scale (f_a) as high as the SUSY GUT scale (M_{GUT} \sim 10^{16} GeV) in the context of the PQMSSM with either an axino or a neutralino LSP. The main problem in non-SUSY models with f_a\sim M_{GUT} is the generation of an overabundance of axion dark matter (\sim f_a^{7/6}) due to vacuum misalignment. We show that once all the components of the axion supermultiplet are included, the upper limit on f_a can be evaded due to large entropy injection from saxion decays. This large entropy injection also dilutes all other quasi-stable relic densities, naturally evading the BBN constraints and solving the gravitino problem. We find that f_a\sim M_{GUT} can be allowed by relic density/BBN constraints provided that the saxion mass m_s> 50 TeV, the initial saxion field value is of order of the PQ scale and the initial axion mis-alignment angle \theta_i\alt 0.05 . These restrictions can be considerably loosened for f_a\sim 10^{15} GeV. The allowed range for the re-heat temperature (T_R) is strongly dependent on the nature of the LSP. For the axino LSP, T_R \gtrsim 10^8 GeV, while for neutralino LSP any value is allowed. In the latter case, f_a\sim M_{GUT} can be more easily accommodated than in the axino LSP scenario. For f_a\sim M_{GUT} in SUSY models, the dark matter abundance should be dominated by axions, albeit with mass m_a\sim 10^{-10} eV, far below the region currently probed by experiment.