Fourth Generation Top Quarks
[I]n a large class of little Higgs and composite Higgs models the fermionic partner of the top quark decays as t' → b W about half of the time. The current limit on the t' mass assuming 100% branching fraction for the t' → b W decay is 525 GeV. For little Higgs et al. the limit is slightly weaker, slightly above 400 GeV (due to the smaller branching fraction) but that is also beginning to feel uncomfortable from the point of view of naturalness of these models.
This result is entirely expected, because a fourth generation electron would be strongly expected to be lighter than a fourth generation top quark, just as each of the other three generations of up quarks are heavier than each of the corresponding three generations of charged leptons. And, while neutrinos are almost impossible to see directly in a detector, and heavy quark decay products can form electrically neutral hadrons that are somewhat hard to see, or can create jets of decay products that are hard to distinguish from know heavy particle decays because there are so many particle detections that have to be combined and because there are many possible scenarios that generate heavy particle decay jets, a very heavy fourth generation electron would generate a very distinctive signal in the data. So it would be surprising if a fourth generation top quark were the first fourth generation particle to be detected.
What about a particle that behaves more or less like a W boson but is heavier? The bounds on this are also getting tighter, but with a twinge of hope, a single outlier event at a TeV scale.
[T]here is no compelling theoretical reasons for such a creature to exist. However they represent a characteristic and clean signature . . . an energetic electron or muon accompanied by missing energy from a neutrino. To tell W' from the ordinary W boson one looks for events with a large transverse mass . . . . Intriguingly, in the muon channel an outlier event with a very large transverse mass of 2.4 TeV is observed in the data. Of course, most likely it's just a fluke[.]
Heavy top-antitop quark pair decays
This search targets heavy (more than 1 TeV) particles decaying to a pair of top quarks, a signature very common in models with a new strongly interacting sector, like composite Higgs or the Randall-Sundrum model. . . . this search relies on fancy modern techniques of studying substructure of jets, in order to identify closely packed jets that could originate from a fast moving top quark. No resonance is observed in the t-tbar spectrum. . . . the LHC sensitivity now reaches the cross sections predicted by popular versions of the Randall-Sundrum model, excluding Kaluza-Klein gluons lighter than about 1.5 TeV.
This is about fifty percent greater than the limits prior to the LHC.
What is a Randall-Sundrum model?
Randall–Sundrum models . . . imagine that the real world is . . . a five-dimensional anti de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes.
The models were proposed in 1999 by Lisa Randall and Raman Sundrum because they were dissatisfied with the universal extra dimensional models then in vogue. Such models require two fine tunings; one for the value of the bulk cosmological constant and the other for the brane tensions. Later, while studying RS models in the context of the AdS/CFT correspondence, they showed how it can be dual to technicolor models.
There are two popular models. The first, called RS1, has a finite size for the extra dimension with two branes, one at each end. The second, RS2, is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model. . . . It involves a finite five-dimensional bulk that is extremely warped and contains two branes: the Planckbrane (where gravity is a relatively strong force; also called "Gravitybrane") and the Tevbrane (our home with the Standard Model particles; also called "Weakbrane"). In this model, the two branes are separated in the not-necessarily large fifth dimension by approximately 16 units (the units based on the brane and bulk energies). The Planckbrane has positive brane energy, and the Tevbrane has negative brane energy. These energies are the cause of the extremely warped spacetime.
A study in 2007 showed that this class of models could be proven or disproven based on searches for "Kaluza-Klein gluons" at LHC.
A minimum mass for gluinos, a particle predicted by SUSY, is based on the latest results, "600-900 GeV depending on how squeezed is the SUSY spectrum."