  Slepton coannihilation is one of the most promising scenarios that can bring
the predicted Dark Matter (DM) abundance in the the Minimal Supersymmetric
Standard Model (MSSM) into agreement with the experimental observation. In this
scenario, the lightest supersymmetric particle (LSP), usually assumed to be the
lightest neutralino, can serve as a Dark Matter (DM) candidate while the
sleptons as the next-to-LSPs (NLSPs) lie close in mass. In our previous studies
analyzing the electroweak (EW) sector of MSSM, a degeneracy between the three
generations of sleptons was assumed for the sake of simplicity. In case of
slepton coannihilation this directly links the smuons involved in the
explanation for $(g-2)_\mu$ to the coannihilating NLSPs required to explain the
DM content of the universe. On the other hand, in well-motivated top-down
models such degeneracy does not hold, and often the lighter stau turns out to
be the NLSP at the EW scale, with the smuons (and selectrons) somewhat heavier.
In this paper we analyze a non-universal slepton mass scenario at the EW scale
where the first two generations of sleptons are taken to be mass-degenerate and
heavier than the staus, enforcing stau coannihilation. We analyze the parameter
space of the MSSM in the light of a variety of experimental data namely, the DM
relic density and direct detection (DD) limits, LHC data and especially, the
discrepancy between the experimental result for $(g-2)_\mu$, and its Standard
Model (SM) prediction. We find an upper limit on the LSP and NLSP masses of
about ~ 550 GeV. In contrast to the scenario with full degeneracy among the
three families of sleptons, the upper limit on the light smuon/selectron mass
moves up by ~ 200 GeV. We analyze the DD prospects as well as the physics
potential of the HL-LHC and a future high-energy $e^+ e^-$ collider to
investigate this scenario further.
