Interpreting Light Scalar Excesses and Heavy Scalar Cascades in the $\mu$-Term Extended NMSSM

Abstract

The hints for a scalar resonance near $95~{\rm GeV}$ in the LEP $b\bar b$ channel and in the LHC diphoton searches remain among the most persistent small deviations in the Higgs sector. At the same time, searches for a heavier resonance decaying into the observed Higgs boson and an additional scalar have become more restrictive, especially after the recent CMS analysis of the $b\bar b b\bar b$ final state. We study these observations in the $\mu$-term extended Next-to-Minimal Supersymmetric Standard Model ($\mu$NMSSM), where a singlet-like CP-even scalar can lie near $95~{\rm GeV}$ and the heavier doublet states can appear around the mass range probed by the CMS searches. After imposing Higgs data, extra Higgs limits, flavor constraints, electroweak precision observables and direct SUSY search bounds, we find viable regions that can accommodate the $95~{\rm GeV}$ diphoton and $b\bar b$ rates within the $2\sigma$ ranges. The viable points fall into two characteristic patterns. One gives a larger diphoton signal through a suppressed $h_s b\bar b$ coupling, while the other gives a larger LEP rate through stronger doublet mixing. The heavy CP-even scalar can decay through $H\to h h_s$ and $H\to h_s h_s$ with rates close to the reach of present and future searches. The CP-odd sector provides an additional channel, $A_2\to h A_1\to 4b$, which can populate the mass region around $(600,400)~{\rm GeV}$ where the latest CMS $4b$ analysis finds its largest local deviation, while remaining below its current limits. For the positive-$\mu$ subset, the inflation-inspired framework admits a gravitino as the lightest supersymmetric particle (LSP) dark matter candidate, with the lightest neutralino acting as the next-to-LSP and is typically long-lived at collider scales.