The number of fermion generations has many effects beyond the mere existence of "3 copies of fermions," including determining scatterings, constraining CP violation, influencing electroweak symmetry breaking, contributing to anomalous magnetic moments, and influencing baryogenesis.

How would the universe differ if there were only 1 generation of fermions, assuming no other standard model couplings changed? (Meaning the electron, 1-neutrino, up, & down Yukawa couplings; the CKM & PMNS phases; $g_1$, $g_2$, & $g_3$; the QCD vacuum angle; and the Higgs $\lambda$ & $\mu$ stay the same.)

Specifically, how would observed particle properties and interaction amplitudes change? And how would those changes affect baryon asymmetry and nucleosynthesis?

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    $\begingroup$ This question (v3) seems too broad. $\endgroup$ – Qmechanic Sep 30 '19 at 18:50
  • $\begingroup$ Compared to this one? I based it on that, but I can narrow it if you like $\endgroup$ – alexchandel Sep 30 '19 at 18:54
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    $\begingroup$ If the question starts to get close votes, you might want to consider that. $\endgroup$ – Qmechanic Sep 30 '19 at 19:05
  • $\begingroup$ Narrowed it, better? $\endgroup$ – alexchandel Sep 30 '19 at 19:59
  • $\begingroup$ Obviously, 1×1 unitary matrix can have any phase $|\delta|=1$. $\endgroup$ – alexchandel Sep 30 '19 at 21:51

As @Qmechanic points out, there is an impossible breadth to the question. I'll try to address the 500lb gorilla in the room first (1), however, at the level of qualitative differences in the fundamental physics. Then outline quantitative ones (2) due to quantum loop effects. You are meant to apply these to particle cosmogenesis (3), which is more open-ended and conjectural, and, properly speaking, "applied physics" based on (1) and (2). All of the answers below are already in your PDG booklet, properly read.

  1. There is only one neutrino species, so the mass eigenstate coincides with the "flavor" one, partnered to the electron — proceed to cut down your cosmological neutrino background in (3) to just it, and redo all your fermion-species-counting arguments for one generation instead of 3. As you pointed out, the Z and W will be substantially narrower, for lack of the missing fermion decay channels. Still, the most important novelty here (justly rewarded by the KM Nobel prize) is that now there is no CP violation driven by fermion mixing. This is so because there is no physical (non-absorbable) fermion phases, neither in the quark, nor in the neutrino sector, Dirac or Majorana. Any conjectured phases are absorbable in the definitions of the fields. This, of course, presents problems for the cosmological baryon asymmetry in (3), where you have to seek novel CP-violating mechanisms, possibly based on multi-Higgsery.
  2. All other higher generation fermions beyond the neutrinos above are weakly unstable, so they mostly affect the quantitative features of fundamental physics through their virtual contributions to loop corrections. So, typically, verify that the QCD β function is now more negative than the one of our 3-generation world. Verify that, the 2-flavor β is larger in magnitude than the 5-flavor such by (6/23)=26%, so scaling will start at lower energies for a fixed nucleon mass. Of course, the missing fermions will provide corrections to all quantities, including QED ones, like the magnetic moments of leptons, etc...
  3. Apply these to particle cosmology where you affect the thermodynamics and the species-counting processes involved, and crucially, you need to introduce a novel CP violating mechanism, and you have a broad array of different worlds, an issue outranging any thinkable sensible scope of this question.
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  • $\begingroup$ Thank you. Would (2) expect the corrected invariant masses of the remaining baryons (N’s & Δ’s) to rise or fall? $\endgroup$ – alexchandel Oct 1 '19 at 15:56
  • $\begingroup$ I don't know. Perhaps looking at the strange sea parton distributions in the respective baryons might be informative, but I'm not sure. My wild guess is mass differences would be accentuated, given the "faster" running of the coupling. $\endgroup$ – Cosmas Zachos Oct 1 '19 at 16:00
  • $\begingroup$ You might survey older lattice baryon spectra and monitor mass differences for quenched, two-, and three-flavor simulations. Unfortunately, my lattice sources cannot easily produce summary plots off the top of their head. $\endgroup$ – Cosmas Zachos Oct 1 '19 at 16:34

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