Probing degenerate heavy Higgs bosons in NMSSM with vector-like particles

In this work, we investigate the degenerate heavy Higgs bosons in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) by introducing vector-like particles. Such an extension is well motivated from the top-down view since some grand unified theories usually predict the existence of singlet scalars and vector-like particles at weak scale. Under the constraints from the LHC and dark matter experiments, we find that (1) the null results of searching for high mass resonances have tightly constrained the parameter space; (2) two degenerate heavy singlet Higgs bosons $h_2$ and $a_1$ can sizably decay to ${\chi }_1^0{\chi }_1^0$ invisibly. Therefore, search for the monojet events through the process $gg\to h_2\mathrm{/}{a}_1(\to {\chi }_1^0{\chi }_1^0)j$ may further test our scenario at the future LHC.