Investigating higgsino dark matter in the semi-constrained NMSSM

In this study, we explore the characteristics of higgsino-dominated dark matter (DM) within the semi-constrained Next-to-Minimal Supersymmetric Standard Model (scNMSSM), covering a mass range from hundreds of GeV to several TeV. We carefully analyzed the parameter space under existing theoretical and experimental constraints to confirm the viability of higgsino-dominated lightest supersymmetric particles (LSPs) with masses between 100 GeV and 4 TeV. Our study examines various DM annihilation mechanisms, emphasizing the significant role of coannihilation with the next-to-lightest supersymmetric particle (NLSP), which includes other higgsino-dominated particles such as $\tilde{\chi}^{0}_2$ and $\tilde{\chi}^{\pm}_1$. We categorize the annihilation processes into three main classes: $\tilde{\chi}_1^{\pm}$ coannihilation, Higgs funnel annihilation, and $\tilde{\tau}_1$ coannihilation, each combines interactions with $\tilde{\chi}_1^{\pm}$. Our results indicate that achieving the correct relic density in heavier higgsino LSPs requires a combination of coannihilation and Higgs funnel mechanisms. We also assess the potential of future experiments, such as XENONnT, LUX-ZEPLIN (LZ), PandaX-xT, and the Cherenkov Telescope Array (CTA), to probe these DM scenarios through direct and indirect detection. In particular, future spin-independent DM detection can cover all samples with the correct DM relic density for $\mu \gtrsim 1300$ GeV. Furthermore, future colliders like the International Linear Collider (ILC) and the Compact Linear Collider (CLIC) are found to exceed the detection capabilities of current hadron colliders, especially for higher mass NLSPs. Notably, CLIC at 3000 GeV is anticipated to thoroughly investigate all samples with insufficient DM relic density for $\mu \lesssim 1300$ GeV.