Why is there no 4th generation of leptons in the standard model?

Question

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?

Answer 1

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.