The Electroweak Supersymmetry (EWSUSY) from the GmSUGRA in the MSSM

Considering the Generalized Minimal Supergravity Model (GmSUGRA) in the Minimal Supersymmetric Standard Model (MSSM), we study the Electroweak Supersymmetry (EWSUSY), where the squarks and/or gluino are heavy around a few TeVs while the sleptons, sneutrinos, Bino, Winos, and/or Higgsinos are light within one TeV. We resolves the $(g_{\mu}-2)/2$ discrepancy for the muon anomalous magnetic moment in the Standard Model (SM) successfully and identifies a parameter space where such solutions also have the electroweak fine-tuning measures $\Delta_{EW}~16.5$ (6$\%$) and $\Delta_{EW}~25$ (4$\%$) without and with the WMAP bounds, respectively. We find that the allowed mass ranges consistent within 3$\sigma$ of the $g-2$ discrepancy for the lightest neutralino, charginos, stau, stau neutrinos, and first two-family sleptons are $[44,390]$ GeV, $[100,700]$ GeV, $[100,700]$, and $[52,700]$ GeV, respectively. Moreover, our solutions satisfy the latest bounds reported by the ATLAS and CMS Collaborations on electroweakinos and sleptons. The colored sparticles such as light stop, gluinos, and the first two-generation squark masses have been found in the mass ranges of $[500, 3000]$ GeV,[1300, 4300] GeV, and $[1800, 4200]$ GeV, respectively. To obtain the observed dark matter relic density for the Lightest Supersymmetric Particle (LSP) neutralino, we have the bino-wino, LSP neutralino-stau, and LSP neutralino-tau sneutrinos coannihilation scenarios, and the resonance solutions such as $A$-pole, Higgs-pole, and $Z$-pole. We identify the higgsino-like LSP neutralino and display its spin-independent and spin-dependent cross sections with nucleons. We present ten benchmark points which can be tested at the up coming collider searches as well.