## Wednesday, April 10, 2013

### Why Three Generations Of Fermions?

Why are there three and only three generations of fermions?  Here is a conjecture.

One heuristic way to think about it is that the mass of a fundamental fermion beyond the first stable first generation and its rate of decay via the weak force are strongly intertwined.  The heavier something is, the faster is decays.  The lighter it is, the less rapidly it decays.

But, nothing can decay via the weak force any faster than the W boson, which facilitates those decays in the Standard Model.

The top quark decays almost, but not quite as quickly as the W boson does, and any particle much heavier would have to decay faster than the W boson.  But, because the W boson is what makes such decays possible, this can't happen.  Therefore, there can be no fundamental particles significantly heavier than the top quark.

Also, there is something to Koide's formula which seems to apply quite accurately to the heavier quark masses and the charged leptons.  If one extends the formula based upon recent data on the mass of the bottom and top quarks and presumes that there is a b', t, b triple, and uses masses of 173.4 GeV for the top quark and 4.190 GeV for the bottom quark, then the predicted b' mass would be 3.563 TeV (i.e. 3,563 GeV) and the predicted t' mass would be about 83.75 TeV (i.e. 83,750 GeV).  If the relationship between decay time for fundamental fermions and mass were extrapolated in any reasonable way to these masses, they would have decay times far shorter than that of the W boson that facilitates this process.  Thus, the bar to fourth generation quarks is similar to the physics that prevents top quarks from hadronizing.

Of course, even if Koide's formula is not correct in this domain, it is suggestive of the kinds of masses for fourth generation quarks that one would expect and the estimated masses need not be very precise to give rise to the same conclusion.

This reasoning also disfavors SUSY scenarios with superpartners that are universally heavier than the top quark, as increasingly seems to be the case for the currently experimentally allowed part of the SUSY parameter space, to the extent that SUSY particle decays and ordinary particle decays both took place via the weak force, which to some extent, is the whole point of SUSY in the first place.  A SUSY theory that decays by means other than the force described in electroweak unification doesn't solve the hierarchy problem which is its reason d'etre.

This reasoning also almost rules out annihilations of fundamental dark matter particles in the 300 GeV to 400 GeV+ mass range as suggested as one possible although quite implausible reading of AMS-02 observations of positron proportions in high energy cosmic rays.  If no fundamental particle can be much heavier than a top quark, than this scenario is ruled out and pair production via gamma-rays interacting with electromagnetic fields are all that remains.

The extension of a Koide triple for charged leptons (a muon, tau, tau prime triple), however, would imply a 43.7 GeV tau prime, which has been excluded at the 95% confidence level for masses of less than 100.8 GeV and with far greater confidence at 43.7 GeV (which would be produced at a significant and easy to measure freuquency in Z boson decays).  This is far from the mass level at which W boson decay rates would impose a boundary on charged lepton mass.  So, one has to infer that fundamental fermion generations, by virtue of some symmetry, are all or nothing affairs and that one cannot have just three generations of quarks, while having four generations of leptons.

This kind of symmetry, if it exists, suggests that the more common sterile neutrino theories are misguided.  Even if there is a massive particle that accounts for dark matter than doesn't interact weakly or electromagnetically or via the strong force, there is no place of it dangling from the neutrinos of the Standard Model at different fermion masses.  Neutrino mass and the source of a dark matter particle very likely are not two birds that can be killed with one unified theoretical solution.

Graviweak unification models, which create a singlet sterile neutrino which is not very tightly bound in mass theoretically within in the gravitational sector, rather than the electroweak sector, thus seem more attractive from this perspective.  These models have only left handed neutrinos and only right handed antineutrinos as a fundamental part of the theory, embracing rather than fighting what observation has told us, and the neutrinos therefore, must acquire mass via the same essential mechanism as all of the other Standard Model fundamental fermions do.

Rather than filling the right handed neutrino gap with mere right handed sterile neutrinos, gravitweak unification models fill the right handed neutrino gap with the entire gravitational sector operating in parallel to the electroweak sector, with the graviton and gravitational fields, a sterile neutrino, an intrasterile neutrino U(1) force, and a gravity sector Higgs boson-like scalar (perhaps the very same Higgs boson extending across both the electroweak and gravitational sectors) that could be attributed to dark energy, the inflaton, interia, or all of the above.