We discuss a ∼ 3 σ signal (local) in the light Higgs-boson search in the diphoton decay mode at ∼ 96 GeV as reported by CMS, together with a ∼ 2 σ excess (local) in the bb final state at LEP in the same mass range. We interpret this possible signal as a Higgs boson in the 2 Higgs Doublet Model with an additional real Higgs singlet (N2HDM). We find that the lightest Higgs boson of the N2HDM can perfectly fit both excesses simultaneously, while the second lightest state is in full agreement with the Higgs-boson measurements at 125 GeV, and the full Higgs-boson sector is in agreement with all Higgs exclusion bounds from LEP, the Tevatron and the LHC as well as other theoretical and experimental constraints. We show that only the N2HDM type II and IV can fit both the LEP excess and the CMS excess with a large ggF production component at ∼ 96 GeV. We derive bounds on the N2HDM Higgs sector from a fit to both excesses and describe how this signal can be further analyzed at the LHC and at future e + e − colliders, such as the ILC.SM is the Minimal Supersymmetric Standard Model (MSSM) [19,20]. In contrast to the single Higgs doublet of the SM, the MSSM by construction, requires the presence of two Higgs doublets, Φ 1 and Φ 2 . In the CP conserving case the MSSM Higgs sector consists of two CP-even, one CP-odd and two charged Higgs bosons. The light (or the heavy) CP-even MSSM Higgs boson can be interpreted as the signal discovered at ∼ 125 GeV [21] (see Refs. [22,23] for recent updates). However, in Ref. [22] it was demonstrated that the MSSM cannot explain the CMS excess in the diphoton final state.Going beyond the MSSM, a well-motivated extension is given by the Next-to-MSSM (NMSSM) (see [24,25] for reviews). The NMSSM provides a solution for the so-called "µ problem" by naturally associating an adequate scale to the µ parameter appearing in the MSSM superpotential [26,27]. In the NMSSM a new singlet superfield is introduced, which only couples to the Higgs-and sfermion-sectors, giving rise to an effective µ-term, proportional to the vacuum expectation value (vev) of the scalar singlet. In the CP conserving case the NMSSM Higgs sector consists of three CP-even Higgs bosons, h i (i = 1, 2, 3), two CP-odd Higgs bosons, a j (j = 1, 2), and the charged Higgs boson pair H ± . In the NMSSM not only the lightest but also the second lightest CP-even Higgs boson can be interpreted as the signal observed at about 125 GeV, see, e.g., [28,29]. In Ref. [17] it was found that the NMSSM can indeed simultaeneously satisfy the two excesses mentioned above. In this case, the Higgs boson at ∼ 96 GeV has a large singlet component, but also a sufficiently large doublet component to give rise to the two excesses.A natural extension of the NMSSM is the µνSSM, in which the singlet superfield is interpreted as a right-handed neutrino superfield [30,31] (see for reviews). The µνSSM is the simplest extension of the MSSM that can provide massive neutrinos through a see-saw mechanism at the electroweak scale. A Yukawa coupling for right-handed ne...

The μνSSM is a simple supersymmetric extension of the Standard Model (SM) capable of describing neutrino physics in agreement with experiments. We perform the complete one-loop renormalization of the neutral scalar sector of the μνSSM with three generation of righthanded neutrinos in a mixed on-shell/DR scheme. We calculate the full one-loop corrections to the neutral scalar masses of the μνSSM. The one-loop contributions are supplemented by available MSSM higher-order corrections. We obtain numerical results for a SM-like Higgs-boson mass consistent with experimental bounds, while simultaneously agreeing with neutrino oscillation data. We illustrate the distinct phenomenology of the μνSSM in scenarios in which one or more right-handed sneutrinos are lighter than the SMlike Higgs boson, which might be substantially mixed with them. These scenarios are experimentally accessible, on the one hand, through direct searches of the right-handed sneutrinos decaying into SM particles, and on the other hand, via the measurements of the SM-like Higgs-boson mass and its couplings. In this way the parameter space of the μνSSM can be probed without the need to propose model dependent searches at colliders. Finally, we demonstrate how the μνSSM can simultaneously accommodate two excesses measured at LEP and LHC at ∼ 96 GeV at the 1σ level, while at the same time reproducing neutrino masses and mixings in agreement with neutrino oscillation measurements. a