Light Neutralino Dark Matter in a Supersymmetric Pati-Salam Framework

We investigate the low-energy phenomenology of the MSSM arising from the supersymmetric $SU(4)_C \times SU(2)_L \times SU(2)_R$ Pati-Salam framework, focusing on neutralino dark matter in bulk annihilation and Higgs/Z-funnel regions. Using a comprehensive parameter scan consistent with radiative electroweak symmetry breaking and a neutralino LSP, we analyze collider, flavor, and dark matter constraints for both signs of {\mu}. To isolate genuine bulk annihilation from coannihilation, we impose the mass-splitting condition $\mathcal{R}_{\tilde{\phi}} \equiv (m_{\tilde{\phi}}-m_{\tilde{\chi}_1^0})/m_{\tilde{\chi}_1^0}\gtrsim 10\%$. We identify a viable bulk region with a bino-like LSP and a light right-handed stau NLSP. These solutions satisfy all experimental constraints, including LHC searches, flavor observables, and the Planck 2018 relic density, predicting upper bounds $m_{\tilde{\chi}_1^0}\lesssim 110~{\rm GeV}$ and $m_{\tilde{\tau}_1}\lesssim 120~{\rm GeV}$. This parameter space lies within the reach of future CEPC and FCC-ee colliders. We also analyze Higgs- and Z-funnel regions. Current direct-detection limits strongly constrain light Higgsino-assisted resonances for {\mu}>0. Conversely, for {\mu}<0, destructive interference in Higgs-mediated scattering suppresses the direct-detection cross section, allowing a viable Z-funnel region to survive below the projected LZ 1000-day sensitivity. These results highlight the negative-{\mu} Pati-Salam framework as a predictive, testable scenario for upcoming dark matter and lepton collider experiments