Supersymmetric explanation of the muon g-2 anomaly with and without stable neutralino

In this paper we explore the possibility of explaining the muon $g-2$ anomaly in various types of supersymmetric extensions of the Standard Model. In particular, we investigate and compare the phenomenological constraints in the MSSM with stable neutralino and the other types of scenarios where the neutralino is unstable. For the latter case we study the Gauge Mediated SUSY Breaking (GMSB) scenario with very light gravitino and the $UDD$-type R-Parity Violating (RPV) scenario. In the MSSM with stable neutralino, the parameter region favoured by the $(g-2)_\mu$ is strongly constrained by the neutralino relic abundance and the dark matter direct detection experiments, as well as by the LHC searches in the lepton plus missing transverse energy channel. On the other hand, the scenarios without stable neutralino are free from the dark matter constraints, while the LHC constraints depend strongly on the decay of the neutralino. We find that in GMSB the entire parameter region favoured by the muon $g-2$ is already excluded if the Next Lightest SUSY Particle (NLSP) is the neutralino, while some regions are still allowed if the NLSP is stau. In the RPV scenario, the LHC constraints are much weaker than the other scenarios and a wide region of the parameter space is still open for the muon $g-2$.