Here is an LHC transverse slice, CMS ,
showing how each detector is crucial in identifying a track or neutral particle coming from the vertex. It is the transverse direction, because the tranverse values of momenta and angles do not change with the lorentz transformations to the center of mass of the p p scattering.
Here is a real event in the 3D detector :
An example of a CMS event with large total transverse energy (ST=2.6 TeV) and high jet multiplicity (9 jets, denoted by light purple cones and lines).
The lines are tracks in the tracking detector and the original event vertex and any vertices on the way in the tracking detectors can be reconstructed.
With these displays in mind:
Invariably, the events that are triggered on have large transverse momentum, so it seems plausible that a jet and a lepton are often detected in nearly the same point of the detector.
Yes, there will be a small probability , which can be gauged by using the monte carlo simulation.
In this scenario, would the jet clustering algorithm combine the hard jet and the lepton (along with all the soft jets within 2R produced from QCD) into one jet?
As you see from the displays, yes, if an electron is hidden within a jet there is a small probability it might be confused, i.e. the algorithm not notice that the electron is stopped in the electromagnetic calorimeter. For muons there is no problem.
If so, is it possible for particle physicists to separate this jet into its constituents so that they can perform useful analysis?
The analysis is statistical. The probabilities of wrong inclusions are calculable by monte carlo. In the case of interesting events, as higgs decays human intervention may try to clear ovelaps.
Further, would this be relatively simple just by looking at the characteristic signals in the EM and hadronic calorimeter?
Confusion about electrons in interesting events would be due to a new vertex appearing, not from the primary event, in the electromagnetic calorimeter, for example.
If the above is true, my final question regards Monte Carlo software which I have found tends to cluster leptons and hadronic jets together indiscriminately, but from my naive viewpoint (above) there is no need to do this because there are clearly distinguishable.
If the tracks have a clear id from the corresponding detectors, there is no confusion , and I do not see why the Montecarlo, which is a tool for simulating events, will do worse.
In analysis of the data, one decides the number of jets and the type of leptons an event sought for should have, and applies the appropriate cuts to data and monte carlo simulations. There is no problem. The efficiencies can be found using the monte carlo data which has the known discrimination of the detectors.
