The Mass Challenge

We have a bit of a puzzle to solve if we're to explain the masses of the heavier particles, in particular muons, pions and beyond. The trouble is that muons are the lightest known particles that are heavier than electrons and are a lot heavier (roughly 200x), weighing in at 105MeV. If we try to model a muon as a composite particle made of electrons and simply add up the constituent masses, we would need 200 or more of them just to make the weight.

Do we really believe that? If so, then why don't we observe a whole plethora of particles with masses in between?

From the work of Malcolm MacGregor, Paolo Palazzi and others, it would appear that there are some patterns to the known particle masses (and lifetimes although we won't go into that here). To cut a long story short, it's possible to come up with a rough mass quantisation based on units of 35MeV:

ParticleMass / MeVMultiple of 35MeV
Muon1053
Neutral Pion1354
Charged Pion1394
Charged Kaon49414
Neutral Kaon49814
Eta Meson54716
Rho Meson77522
Proton93827
Neutron93927
Eta Prime95727
Lambda Baryon111532
Sigma Baryon118934
Delta Baryon123235

The challenge is to come up with an explanation for why particles occur with these masses and not in between.

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