  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.
