Aspects of the WIMP quality problem and R-parity violation in natural supersymmetry with all axion dark matter

In supersymmetric models where the mu problem is solved via discrete R-symmetries, then both the global U(1)_{PQ} (Peccei-Quinn, needed to solve the strong CP problem) and R-parity conservation (RPC, needed for proton stability) are expected to arise as accidental, approximate symmetries. Then in some cases, SUSY dark matter is expected to be all axions since the relic lightest SUSY particles (LSPs) can decay away via small R-parity violating (RPV) couplings. We examine several aspects of this {\it all axion} SUSY dark matter scenario. 1. We catalogue the operator suppression which is gained from discrete R-symmetry breaking via four two-extra-field base models. 2. We present exact tree-level LSP decay rates including mixing and phase space effects and compare to results from simple, approximate formulae. 3. Natural SUSY models are characterized by light higgsinos with mass ~100-350 GeV so that the dominant sparticle production cross sections at LHC14 are expected to be higgsino pair production which occurs at the 10^2-10^4 fb level. Assuming nature is natural, the lack of an RPV signal from higgsino pair production in LHC data translates into rather strong upper bounds on nearly all trilinear RPV couplings in order to render the SUSY signal (nearly) invisible. Thus, in natural SUSY models with light higgsinos, the RPV-couplings must be small enough that the LSP has a rather high quality of RPC.