This study systematically examines the parameter space of GNMSSM with a light CP-odd Higgs boson $a_1$, emphasizing the exotic decay $h_{125}\to a_1a_1$ under recent Higgs data constraints. Firstly, We scan the parameter space under the basic constraints from \textsf{HiggsSignals-2.6.2} and \textsf{HiggsBounds-5.10.2}, and then further filter the surviving parameter points using constraints from the LHC direct Higgs searches and \textsf{HiggsTools}. Comparative analysis demonstrates that the code \textsf{HiggsTools} imposes stringent constraints compared to legacy versions of \textsf{HiggsSignals-2.6.2} and \textsf{HiggsBounds-5.10.2}. Moreover, its exclusion capacity notably exceeds the direct individual decay channel searches. Through comparative analysis of the two types of constraints (\textsf{HiggsSignals} and \textsf{HiggsBounds}) embedded in the HiggsTools, we found that the constraints from \textsf{HiggsBounds} are the most stringent. Almost all parameter points excluded by \textsf{HiggsSignals} and the individual decay channel analyses at the LHC can also be excluded by \textsf{HiggsBounds}. This is because \textsf{HiggsBounds} provides direct constraints, while \textsf{HiggsSignals} imposes indirect constraints for the searches of non-SM Higgs bosons. In the $h_2$ scenario, due to the the kinematic accessibility of the exotic decay channel $h_2 \to h_1h_1$, \textsf{HiggsSignals} can also exclude the parameter points with smaller values of $Br(h\to a_1 a_1\to \tau\tau/\mu\mu bb)$. Despite rigorous experimental limitations constraining the light CP-odd Higgs scenario, our comprehensive investigation still reveals viable parameter regions, which opens new avenues for future exploration of light Higgs phenomenology.
Comment: 19 pages, 7 figures