The Standard Model of particle physics splits both the leptons and the quarks into three generations, with mass and instability going up from the first to the third generation. These are normally displayed together, on the same rows or columns of the table of fundamental particles:

This makes some sense: each charged lepton is tied to its neutrino in most Feynman vertices it appears in, and the quarks are linked to each other by their charges, if nothing else. However, I can't think of any way in which the SM formally links, say, muons and strange quarks. It's there some explicit link with generation-specific interactions? Or is it just coincidence that there's three rungs in both ladders with increasing mass on both?

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    $\begingroup$ There is nothing, to my knowledge, preventing interchange of any two green columns (doublets) keeping the purple ones unchanged, and vice versa. Historically, they were ordered in mass, from left to right, But for heavily mixed neutrino states that classification is at best confusing. "Generation rank" is not a good quantum number! $\endgroup$ – Cosmas Zachos Feb 18 '17 at 14:41
  • $\begingroup$ Historically the linkage was the result of Gellmann"s physical intuition. I heard him speak of this linkage right after the discovery of the tau and charmed quark and this led him to predict the b and t wuarks $\endgroup$ – Lewis Miller Dec 9 '19 at 1:54
  • $\begingroup$ Comtinued; I don't remember him giving any physical reason for the linkage. $\endgroup$ – Lewis Miller Dec 9 '19 at 1:57

Yes, they are very strongly linked. On top of the classification in generations, and on top of writing the classical field theory action for the Standard Model, the Standard Model should be a well behaved quantum theory. In particular, quantum gauge theories with chiral (left handed) fermions lead, in general, to appearance of gauge anomalies. If they appear, they render the original theory invalid, if considered as a quantum theory. It turns out, that one full generation -- neutrino-charged lepton-up and down quarks leads to cancellation of the anomaly, while partial generation do not, rendering the theory invalid as quantum theory. See discussion at stackexchange, or an example of a lecture on this topic.

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    $\begingroup$ I fear that is not the OPs question: he is asking why the lepton doublet of the 2nd generation, for instance, is tied to the quark one, and not to the quark doublet of the 3rd one, and vice versa. Anomalies cancel within each generation, but there is no intrinsic "secondness" in the second one, for instance. People have simply put these generations together out of lepton and quarks historically, so therefore ordered in mass. $\endgroup$ – Cosmas Zachos Feb 18 '17 at 14:36
  • $\begingroup$ Hmm. In this form it is actually wrong to say that the generations are separte at all in SM. That is, in the mass basis both quarks and leptons (neutrinos) are mixed between generations. Moreover, the mixing is rather strong, especially for neutrinos. So, the ordering of the three lepton pairs and quark pairs is indeed arbitrary for pure SM, but the existence of three of both is not. $\endgroup$ – Fedxa Feb 18 '17 at 15:00
  • $\begingroup$ My point exactly. Because quark mixing is small, people could, and do!, talk about weak and mass eigenstates linked, sloppily. But because neutrino mixing is huge, talking about masses of $\nu_e$, etc is "not even wrong". $\endgroup$ – Cosmas Zachos Feb 18 '17 at 15:13
  • $\begingroup$ @Cosmas' first comments gets the essence of my question correctly. I was unaware of quark mixing, though. Is there a similar mass/flavour mixing of the charged leptons? $\endgroup$ – Emilio Pisanty Feb 19 '17 at 16:18
  • $\begingroup$ @Emilio Here is my own answer to the issue: they do mix, but you need to anchor to some mass eigenstates, so we call e,μ,τ mass eigenstates , and their weak isopartners are then mixtures of neutrino mass eigenstates. When we produce charged leptons out of a neutrino mass eigenstate, such mixed states which oscillate so rapidly on acount of their high masses that, by the time they hit the detector, they have decohered to mixtures of charged lepton mass eigenstates. $\endgroup$ – Cosmas Zachos Feb 19 '17 at 16:42

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