96 GeV diphoton excess in 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 dark matter (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 bb excess at LEP-II and the continuously observed 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 supersymmetry (SUSY) search at the LHC.