The 96 GeV Diphoton Excess in the Seesaw Extensions of the Natural NMSSM

The Next-to Minimal Supersymmetric Standard Model (NMSSM) with a Type-I seesaw mechanism extends the NMSSM by three generations of right-handed neutrino fields to generate neutrino mass. As a byproduct it renders the lightest sneutrino as a viable DM candidate. Due to the gauge singlet nature of the DM, its scattering with nucleon is suppressed in most cases to coincide spontaneously with the latest XENON-1T results. Consequently, broad parameter spaces in the Higgs sector, especially a light Higgsino mass, are resurrected as experimentally allowed, which makes the theory well suited to explain the long standing $b \bar{b}$ excess at LEP-II and the continuously observed $\gamma \gamma$ excess by CMS collaboration. We show by both analytic formulas and numerical results that the theory can naturally predict the central values of the excesses in its broad parameter space, and the explanations are consistent with the Higgs data of the discovered Higgs boson, $B-$physics and DM physics measurements, the electroweak precision data as well as the LHC search for sparticles. Part of the explanations may be tested by future DM experiments and the SUSY search at the LHC.