Rather general considerations of the string theory landscape imply a mild statistical draw towards large soft SUSY breaking terms tempered by the requirement of proper electroweak symmetry breaking where SUSY contributions to the weak scale are not too far from m _ { weak } \sim 100 GeV .
Such a picture leads to the prediction that m _ { h } \simeq 125 GeV while most sparticles are beyond current LHC reach .
Here we explore the possibility that the magnitude of the Peccei-Quinn ( PQ ) scale f _ { a } is also set by string landscape considerations within the framework of a compelling SUSY axion model .
First , we examine the case where the PQ symmetry arises as an accidental approximate global symmetry from a more fundamental gravity-safe \mathbb { Z } _ { 24 } ^ { R } symmetry and where the SUSY \mu parameter arises from a Kim-Nilles operator .
The pull towards large soft terms then also pulls the PQ scale as large as possible .
Unless this is tempered by rather severe ( unknown ) cosmological or anthropic bounds on the density of dark matter , then we would expect a far greater abundance of dark matter than is observed .
This conclusion can not be negated by adopting a tiny axion misalignment angle \theta _ { i } because WIMPs are also overproduced at large f _ { a } .
Hence , we conclude that setting the PQ scale via anthropics is highly unlikely .
Instead , requiring soft SUSY breaking terms of order the gravity-mediation scale m _ { 3 / 2 } \sim 10 - 100 TeV places the mixed axion-neutralino dark matter abundance into the intermediate scale sweet zone where f _ { a } \sim 10 ^ { 11 } -10 ^ { 12 } GeV .
We compare our analysis to the more general case of a generic SUSY DFSZ axion model with uniform selection on \theta _ { i } but leading to the measured dark matter abundance : this approach leads to a preference for f _ { a } \sim 10 ^ { 12 } GeV .