Why is there no 4th generation of leptons in the standard model? Is there any explanation, as to why they don't exist? More precisely, is there any theoretical restriction to having only 3 generations or is there any possibility that there could be more than 3 generations which we might see at higher energy?

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    $\begingroup$ Depends on 1) what you mean by "why", and 2) what counts as an "explanation". If by "why" you mean "how do we know", then there are a few different experimental signatures that we use to constrain the number of generations. If by "explanation" you include unverified beyond-the-Standard-Model theories, then yes, there are plenty. $\endgroup$ – probably_someone Oct 31 at 6:05
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    $\begingroup$ The simple answer is ; the model models reality, extra leptons have not been observed. If a new model appears to embed the standard model and predict new letons people will start experiments to find them. $\endgroup$ – anna v Oct 31 at 6:10
  • $\begingroup$ I think the OP is asking if there is any theoretical reason. For example, we have theoretical reasons why the antielectron does exist (C symmetry) and why tachyons don't (they appear as unstable solutions in QFT). $\endgroup$ – Ben Crowell Oct 31 at 12:58
  • $\begingroup$ Yes, I was asking if there are any theoretical restriction to having only 3 generation of leptons or there might be more than 3 which we might observe at higher energy? $\endgroup$ – royabhi Nov 1 at 7:43
  • $\begingroup$ @royabhi I vaguely remembered that extra dimension models gave some arguments about this but I'm not so sure. My first thought was that even if there's extra generations, the energy required to be able to observe them would be too high. And any impact on the phenomenology of this would be absorbed into the couplings of existing leptons. I can't think of any symmetry constraints and I would doubt if anomaly has anything to do with it. But I'm extremely unfamiliar with the matter so correct me if I'm wrong. $\endgroup$ – Turgon Nov 2 at 7:45

I can answer "How we know", because I (and others) personally did (one of) the experiments.

We had a machine (the Large Electron-Positron collider - LEP) that could apply precise amounts of energy to the centre of a particle detector (in our case ALEPH). As we tuned the energy, we could watch $Z^0$ bosons emerge and decay. The rate of production varies as you change the energy so you get a bell-curve with a peak at 91.2 GeV. The shape of the curve tells you how many ways the $Z^0$ can decay (called channels). If there are many channels, you get a wide flattish curve. If there are few channels the curve is sharper and taller.

We then got computer predictions of what the curve would look like with different numbers of neutrino generations (2, 3, 4, etc.) and checked to see which prediction fitted the data best. The answer was, very clearly, n=3.

So we could conclude that, if there is a fourth generation of particles, its lightest member (presumably the neutrino) must have a mass greater than half (since you have to make them in pairs) the $Z^0$ mass - 45.6 Gev. That's a pretty heavy neutrino...

This is a very good summary.

  • $\begingroup$ Yes, indeed, it was a good summary. I want to ask further, is there any theoretical restriction to having only 3 or there might be more than 3 which we might see at higher energy? $\endgroup$ – royabhi Nov 1 at 7:40
  • $\begingroup$ Sadly, I'm not much of a theoretician... AFAIU, the Standard Model is based on 3 generations. You could certainly extend the Model into 4 or more, but you'd probably need supersymmetry. This is a good read: symmetrymagazine.org/article/august-2015/… P.s., If you liked my answer, you might consider up-voting? (it's how we gain credit on SE). $\endgroup$ – Oscar Bravo Nov 1 at 7:50

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