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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?)

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If Higgs counts as "new particle", then there is. Also, there are lots of new particles at the scale of grand unification. And there may be an infinite tower of massive Kaluza-Klein particles if extra dimensions exist. – felix Apr 23 '11 at 4:57
Well, this would be a bound on the mass of a particular particle. I'd be interested in whether there's a bound for the mass of any particle. – Lagerbaer Apr 23 '11 at 4:58
up vote 3 down vote accepted

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.

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Coming from a phenomenologist (in training :-p), I'm inclined to agree - at least, I can't think of anything we know to be true that would provide an upper mass limit. But I'm hesitant to definitively say "no" in case there's something I just don't know about or am forgetting. – David Z Apr 23 '11 at 5:22

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.

Regards, Hans

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In string theory there are massive excitations of arbitrarily large masses. So it's not correct to claim that main stream physics constraints particles masses to be below the Planck mass. – felix Apr 26 '11 at 5:57
@felix: but the heavier excitations are classified as black holes, not elementary particles. There is a continuous transition between elementary particle and black hole in string theory. – Ron Maimon Dec 31 '11 at 12:31

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