We study to which extent SUSY extensions of the Standard Model can describe the excess of events of 3.0 standard deviations observed by ATLAS in the on-Z signal region, respecting constraints by CMS on similar signal channels as well as constraints f
rom searches for jets and E^{miss}_T. GMSB-like scenarios are typically in conflict with these constraints, and do not reproduce well the shape of the E^{miss}_T distribution of the data. An alternative scenario with two massive neutralinos can improve fits to the total number of events as well as to the H_T and E^{miss}_T distributions. Such a scenario can be realised within the NMSSM.
In the presence of a light singlino-like LSP in the NMSSM, the missing transverse energy - MET - signature of squark/gluino production can be considerably reduced. Instead, a pair of Higgs bosons is produced in each event. We propose benchmark points
for such scenarios, which differ in the squark and gluino masses, and in their decay cascades. Events for these points are simulated for the run II of the LHC at 13 TeV centre of mass energy. After cuts on the transverse momenta of at least four jets, and requiring two tau-leptons from one Higgs decay, we find that the invariant mass of two b-jets from the other Higgs decay shows clear peaks above the background. Despite the reduced MET, this search strategy allows to see signals for sufficiently large integrated luminosities, depending on the squark/gluino masses.
A light singlino in the NMSSM can reduce considerably the missing transverse energy at the end of sparticle decay cascades; instead, light NMSSM-specific Higgs bosons can be produced. Such scenarios can be consistent with present constraints from the
LHC with all sparticle masses below ~1 TeV. We discuss search strategies, which do not rely on missing transverse energy, for such scenarios at the next run of the LHC near 14 TeV.
We discuss NMSSM scenarios in which the lightest Higgs boson $h_1$ is consistent with the small LEP excess at about 98 GeV in $e^+e^- to Zh$ with $hto banti b$ and the heavier Higgs boson $h_2$ has the primary features of the LHC Higgs-like signals a
t 125 GeV, including an enhanced $gammagamma$ rate. Verification or falsification of the 98 GeV $h_1$ may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under consideration.
