Pair production of Higgs boson in NMSSM at the LHC with next-to-lightest CP-even Higgs boson being SM-like

The next-to-minimal supersymmetric standard model (NMSSM) more naturally accommodates a Higgs boson with a mass of approximately 125 GeV than the minimal supersymmetric standard model (MSSM). In this work, we assume that the next-to-lightest CP-even Higgs boson $h_2$ is the SM-like Higgs boson $h$, whereas the lightest CP-even Higgs boson $h_1$ is dominantly singlet-like. We discuss the $h_1h_1$, $h_2h_2$, and $h_1h_2$ pair production processes via gluon-gluon fusion at the LHC for an collision energy of 14 TeV, and we consider the cases in which one Higgs boson decays to $b\bar b$ and the other one decays to $\gamma\gamma$ or $\tau^+\tau^-$. We find that, for $m_{h_1} \lesssim$ 62 GeV, the cross section of the $gg \to h_1 h_1$ process is relatively large and maximally reaches 5400 fb, and the production rate of the $h_1h_1\to b\bar b \tau^+\tau^-$ final state can reach 1500 fb, which make the detection of this final state possible for future searches of an integrated luminosity of 300 and 3000 $fb^{-1}$. This is mainly due to the contributions from the resonant production process $pp\to h_2\to h_1h_1$ and the relatively large branching ratio of $h_1\to b\bar b$ and $h_1\to\tau^+\tau^-$. The cross sections of the $pp \to h_2h_2$ and $pp \to h_1 h_2$ production processes maximally reach 28 fb and 133 fb, respectively.