One possible outcome of the collision experiments at LHC is the discovery of new elementary particles with large mass. Is there a theoretical way to derive an upper bound on the mass of elementary particles? For example, we have the electron, the muon and the tau particle. Can we be sure that there are no heavier elementary fermions with charge $e$? (Maybe there are some symmetry arguments?)
This needs an input from a theoretician. From my experimentalist's view point of the matter, the answer is "probably not" .
We do have the standard model, and it is symmetry based and masses are limited within this symmetry. Nevertheless, there are tantalizing indications of physics beyond the standard model, from deviations of measurements and theoretical calculations in several quantities.
Higher symmetries are envisioned, as supersymmetry, and indeed there, there would be an upper limit in the masses of all the particles, except that theoreticians will embed it into strings which are another ball park, where even a black hole can be considered an excitation on the string. So no upper bound calculable.
This question then will be answered by the Theory Of Everything, strings, according to string theorists. Or we will keep opening russian dolls to higher and higher symmetries and particles, as fans of the unpopular composite theories contend, until an alternate TOE tells us whether we have reached a top mass.
A candidate for such an upper mass would be the Planck mass, at least from well accepted main stream physics. It is the mass where the Compton wavelength and Schwarzschild radius become equal.