The CMS Collaboration has recently reported some excess events in final states with electrons and jets, in searches for leptoquarks and $W$ bosons. Although these excesses may be due to some yet-to-be-understood background mismodeling, it is useful t
o seek realistic interpretations involving new particles that could generate such events. We show that resonant pair production of vector-like leptons that decay to an electron and two jets leads to kinematic distributions consistent with the CMS data.
We present a new strategy to uncover light, quasi-degenerate Higgsinos, a likely ingredient in a natural supersymmetric model. Our strategy focuses on Higgsinos with inter-state splittings of O(5-50) GeV that are produced in association with a hard,
initial state jet and decay via off-shell gauge bosons to two or more leptons and missing energy, $pp to j + text{MET}, + 2^+, ell$. The additional jet is used for triggering, allowing us to significantly loosen the lepton requirements and gain sensitivity to small inter-Higgsino splittings. Focusing on the two-lepton signal, we find the seemingly large backgrounds from diboson plus jet, $bar tt$ and $Z/gamma^* + j$ can be reduced with careful cuts, and that fake backgrounds appear minor. For Higgsino masses $m_{chi}$ just above the current LEP II bound ($mu simeq 110,$) GeV we find the significance can be as high as 3 sigma at the LHC using the existing 20 fb$^{-1}$ of 8 TeV data. Extrapolating to LHC at 14 TeV with 100 fb$^{-1}$ data, and as one example $M_1 = M_2 = 500$ GeV, we find 5 sigma evidence for $m_{chi} lesssim, 140,$ GeV and 2 sigma evidence for $m_{chi} lesssim, 200,$ GeV . We also present a reinterpretation of ATLAS/CMS monojet bounds in terms of degenerate Higgsino ($delta m_{chi} ll 5,$) GeV plus jet production. We find the current monojet bounds on $m_{chi}$ are no better than the chargino bounds from LEP II.
We show that a muon collider is ideally suited for the study of heavy H/A scalars, cousins of the Higgs boson found in two-Higgs doublet models and required in supersymmetric models. The key aspects of H/A are: (1) they are narrow, yet have a width-t
o-mass ratio far larger than the expected muon collider beam-energy resolution, and (2) the larger muon Yukawa allows efficient s-channel production. We study in detail a representative Natural Supersymmetry model which has a 1.5 Tev H/A with $m_H$- $m_A$ = 10 Gev. The large event rates at resonant peak allow the determination of the individual H and A resonance parameters (including CP) and the decays into electroweakinos provides a wealth of information unavailable to any other present or planned collider.
