Improved $(g-2)_\mu$ measurement and singlino dark matter in $\mu$-term extended $\mathbb{Z}_3$-NMSSM

Abstract

Very recently, a Fermilab report of muon $g-2$ showed a $4.2\sigma$ discrepancy between it and the standard model (SM) prediction. Motivated by this inspiring result and the increasing tension in supersymmetric interpretation of the anomalous magnetic moment, it is argued that in the general next-to-minimal supersymmetric standard model (GNMSSM), a singlino-dominated neutralino can act as a feasible dark matter (DM) candidate in explaining the discrepancy naturally. In this case, the singlino-dominated DM and singlet-dominated Higgs bosons can form a secluded DM sector with $\tilde{\chi}_1^0\tilde{\chi}_1^0 \to h_s A_s$ responsible for the measured DM relic abundance. when $m_{\tilde{\chi}_1^0} \gtrsim 150~{\rm GeV}$ and the Yukawa coupling $\kappa$ is around $0.2$. This sector communicates with the SM sector by weak singlet-doublet Higgs mixing, so the scatterings of the singlino-dominated DM with nucleons are suppressed. Furthermore, due to the singlet nature of the DM and the complex mass hierarchy, sparticle decay chains in the GNMSSM are lengthened in comparison with the prediction of the minimal supersymmetric standard model. These characteristics lead to sparticle detection at the Large Hadron Collider (LHC) being rather tricky. This study surveys a specific scenario of the GNMSSM, which extends the $\mathbb{Z}_3$-NMSSM by adding an explicit $\mu$-term, to reveal the features. It indicates that the theory can readily explain the discrepancy of the muon anomalous magnetic moment without conflicting with the experimental results in DM and Higgs physics, and the LHC searches for sparticles.