Constraining the light Higgs bosons in the GNMSSM with recent Higgs data

The search for light scalar and pseudoscalar particles provides a promising avenue for probing physics beyond the Standard Model (SM). In this study, we investigated the exotic decay channels of the 125 GeV SM-like Higgs boson into pairs of light CP-odd ($a_s$) or CP-even ($h_s$) Higgs bosons within the framework of the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM). A comprehensive parameter space scan is performed using the MultiNest algorithm, incorporating constraints from $\mathsf{\text{HiggsSignals-2.6.2}}$, $\mathsf{\text{HiggsBounds-5.10.2}}$, and ATLAS experimental searches, under two distinct scenarios where either the lightest ($h_1$) or next-to-lightest ($h_2$) CP-even state is the observed Higgs boson ($h$). Our results demonstrate that $\mathsf{\text{HiggsBounds}}$ imposes the most stringent exclusion limits due to its sensitivity to direct searches for non-SM Higgs bosons. In the $h_2$ scenario, $\mathsf{\text{HiggsSignals}}$ can additionally exclude regions with suppressed exotic branching ratios (e.g., $Br(h\to a_s{a}_s\to \tau \tau bb)\le 2.5\mathrm{\%}$), due to its sensitivity to indirect deviations caused by the kinematically enhanced decay $h\to h_s{h}_s$. Under combined constraints from $\mathsf{\text{HiggsTools}}$, $h$ must retain at least 93% SM-like component ($V_h^{\text{SM}}\ge 0.93$) with no more than 32% singlet admixture ($V_h^{\text{S}}\le 0.32$); in the $h_2$ case, the lightest scalar $h_s$ exhibits high singlet purity ($V_{h_s}^{\text{S}}\ge 0.94$). Furthermore, dark matter (DM) phenomenology indicates that singlino- or higgsino-dominated DM is viable in the $h_1$ scenario, with dominant annihilation channels including ${\tilde{\chi }}_1^0{\tilde{\chi }}_1^0\to h_s{a}_s$ for singlino-like DM and chargino co-annihilation for higgsino-like DM, whereas the $h_2$ scenario favors higgsino-dominated DM.