Search for a lighter Higgs Boson in the Next-to-Minimal Supersymmetric Standard Model

After the discovery of the Higgs boson with mass at approximately 125 $GeV$ at the LHC, many studies both from the theoretical and experimental sides have been performed to search for a new Higgs Boson lighter than the 125 $GeV$ Higgs boson. We explore the possibility of constraining a lighter neutral scalar Higgs boson $h_{1}$ and a lighter pseudo-scalar Higgs boson $a_{1}$ in the Next-to-Minimal Supersymmetric Standard Model by restricting the next-to-lightest scalar Higgs boson $h_{2}$ to be the LHC observed Higgs boson after the phenomenological constraints and the constraints from experimental measurements. Such lighter particles are not yet completely excluded by the latest results of the search for a lighter Higgs boson with the diphoton decay channel from LHC data. Our results show that for a lighter scalar Higgs boson some new constraints on the Next-to-Minimal Supersymmetric Standard Model could be obtained at the LHC if such a search is performed by the experimental collaborations with more data. The discovery potential of other interesting decay channels of such a lighter neutral scalar and a pseudo-scalar particle are also discussed.