[oyoman]

I hope to provide some perspective : The Standard Model (SM) is based on a specific number of free parameters, such as the masses of elementary particles, the number of generation of families (quarks, leptons/neutrinos) etc. Those parameters are not fixed by the theoritical model, in the SM they are free (I hope it is clear enough). They are inferred from the experimental data so that we have defined what they are now.

The number of family of neutrinos was deduced for the first time in LEP experiments (in the 90s, the predecessor of LHC at CERN) : It was not known before whether there were 2, 3, or 4 family of neutrinos. If you want to learn more : http://pdg.lbl.gov/2020/reviews/rpp2020-rev-light-neutrino-t... a review about this subject. In summary, the combined result from LEP experiments is N_neutrinos = 2.984 +- 0.008. If you are interested, you can see the experimental plot that shows the fit and the difference between of a SM with 2, 3, and 4 neutrinos : https://arxiv.org/pdf/hep-ex/0509008.pdf Page 36 Figure 1.13, the data points are in red with their error bars (extremely important to pay attention to them and their size !) and the curves are the SM prediction for 2, 3, and 4 neutrinos.

In my opinion, this is a very nice plot that shows how different is the SM with 4 neutrino. This is why the SM is with 3 neutrinos and not otherwise, it is because the experimental data that were used to infer all the free parameters of the SM. The last ones were related the Higgs boson, and now everything is fixed.

To accommodate a 4th neutrino, then we would need to go beyond SM.

[cjfd]

This seems to be assuming that the neutrinos are massless, or at least have a mass quite a bit smaller than the Z particle. It could be that there is a fourth generation where both lepton and neutrino are heavier than the Z particle, no?

[evanb]

In the Standard Model as written in the 1970s the neutrinos had to be exactly massless. We now have evidence that neutrinos aren't exactly massless, but they're very VERY light. Like, absurdly light. We still don't know the absolute scale of the neutrino masses, we know from mixing that they're damn small and from cosmology that the sum of all three masses is less than the mass of the electron / a million.

It is logically possible that the neutrino of the fourth generation is very heavy. In that case

- the constraint on the number of neutrinos from collider experiments is relaxed because the ultra-heavy neutrino's contribution to the observable would be extremely suppressed (because the collision energy was too low to be sensitive).

- the cosmological constraints are relaxed because the heavy neutrinos are already frozen out by the time of the electroweak phase transition in the early universe.

- the mixing constraints... well, right now it seems that the mixing matrix between the generations is unitary---there's no "leak" into a fourth generation. But our experimental precision is mediocre because precisely measuring the mixing is difficult (though there are experiments under way). It is also logically possible for there to be a fourth generation but that the neutrino doesn't mix at all---its mixing with the lighter neutrinos is precisely 0. While it's perfectly possible logically, we physicists do not like this kind of "fine tuning" without some explanation of how it could happen. In the SM the neutrino masses/mixings are input parameters, not things determined dynamically---they are axioms, so to speak. So any explanation of the mixing being really small would need to invoke more beyond-the-Standard-Model physics than "it's the same but there's a fourth generation".