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Origin of lepton/quark generations?

In the standard model (and in nature), Fermions appear in different generations, or flavors. Besides up and down quarks and electrons, there are strange, charm, muon, tau, etc.. I am wondering if there is any theoretical explanation for the existence of heavier generations.

What I'd like to know is especially: Why are there different, heavier copies of $e$, $u$, $d$? What makes these particles different from their lighter relatives besides their mass? What is flavour, where does it come from, and why is it approximately conserved (at least for charged leptons)?


Note: I'm posting this question as a follow up on my previous one "Origin of lepton/quark generations?", which didn't reallty get the type of answers I was expecting. Sorry if the old question caused some confusion. To be clear, I'm not asking:

But rather: What possible theoretical explanation is there that our universe exibits flavor quantum numbers, and maybe how are they are related to particle masses?

Conceivable (although probably wrong) answers would be along the line of:

  • "Because electrons and up quarks have substructure, and muons and charm quarks are the first excited states."
  • "In XY theory, $e$, $\mu$ and $\tau$ are actually the same at first order, but the thingamajig symmetry is broken at low energies."
  • "It is explained by string theory, if your vacuum has such-and-such properties it comes out naturally."
  • "It's accidential in the SM and just experimentally observed, but in SU(...) GUTs it is a prediction."
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Note that some things like "strangeness" are conserved as well (only in some cases). Unfortunately I'm not clear enough in the topic to write up a whole answer, but interesting question! :) –  Manishearth Dec 6 '12 at 14:28
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flavour is a useful concept exactly because it is (approximately) conserved for charged leptons. Keep in mind that things like 'flavour' are concepts we (humans) introduced to describe observed effects in nature and make quantitative predictions for future experiments. If one day a better theory is discovered (e.g. fewer parameters while still being consistent with observation), it may or may not have the concept of flavour. –  Andre Holzner Dec 6 '12 at 14:50
    
@AndreHolzner: Right. It seems that flavor is something fundamental and real, and thus a better theory might explain it. "Oh, that's a manifestation of the XYZ symmetry.". It might as well go away as a fundamental concept, like nuclear isospin, when a new theory comes along. I'm just looking for either kind of theory here. Some brilliant theorist must have thought of some crazy theory to explain this, they always do :-) –  jdm Dec 6 '12 at 15:04
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Could you clarify how this differs from the earlier one. By extension to quark flavor as well, or is there something I'm missing. Not that I'm planning on closing this, but there is a pending vote to close so someone is thinking that way. –  dmckee Dec 6 '12 at 16:16
    
@dmckee: I want to know how people are trying to explain the origin of flavor. i.e. the conserved thing that makes muons different from electrons. Can it be a broken symmetry? Substructure? That's what I tried to ask both times. However, the other question was universally misinterpreted as something like "why three generations? (how do we know the fact, and what phenomena depend on it?)". –  jdm Dec 6 '12 at 16:34
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marked as duplicate by Qmechanic, Sklivvz, David Z Jan 1 '13 at 7:44

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1 Answer

Looking thru Weinberg, Zee, Veltman and others, there is practically a consensus that there is no satisfactory theoretical approach to this nasty question. But way back in the sixties I heard a talk where the guy argued that one could use complex octonions to define a collection of oscillators which exhibit a 'generational' pattern, and tied the number of fermion generations to the dimensionality of space. But I have not seen a paper on it, and back then it was all handwaving anyway, but vaguely remember his conjecture that there are three generations - perhaps remarkable because it was 1966.

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