Coupled Boltzmann computation of mixed axion neutralino dark matter in the SUSY DFSZ axion model

The supersymmetrized DFSZ axion model is highly motivated not only because it offers solutions to both the gauge hierarchy and strong CP problems, but also because it provides a solution to the SUSY mu problem which naturally allows for a Little Hierarchy. We compute the expected mixed axion-neutralino dark matter abundance for the SUSY DFSZ axion model in two benchmark cases-- a natural SUSY model with a standard neutralino underabundance (SUA) and an mSUGRA/CMSSM model with a standard overabundance (SOA). Our computation implements coupled Boltzmann equations which track the radiation density along with neutralino, axion (produced thermally (TH) and via coherent oscillations (CO)), saxion (TH- and CO-produced), axino and gravitino densities. In the SUSY DFSZ model, axions, axinos and saxions go through the process of freeze-in-- in contrast to freeze-out or out-of-equilibrium production as in the SUSY KSVZ model-- resulting in thermal yields which are largely independent of the re-heat temperature. We find the SUA case with suppressed saxion-axion couplings (\xi=0) only admits solutions for PQ breaking scale f_a~< 5\times 10^{12} GeV where the bulk of parameter space tends to be axion-dominated. For SUA with allowed saxion-axion couplings (\xi =1), then f_a values up to ~ 2\times 10^{14} GeV are allowed. For the SOA case, almost all of SUSY DFSZ parameter space is disallowed by a combination of overproduction of dark matter, overproduction of dark radiation or violation of BBN constraints. An exception occurs at very large f_a~ 10^{15}-10^{16} GeV where large entropy dilution from CO-produced saxions leads to allowed models.