Thursday, September 1, 2011

Musing On Potential Fourth Generation Fermion Masses

We can say with certainty that any fourth generation quarks of either the up type or down type, would be heavier than a top quark.

It would also follow that like a top quark these would be too heavy to hadronize and would probably have a top quark like decay dominated by decays to the next lightest quark. A b' decay would be dominated by the b' to t to b channel. A t' decay would be dominated by a t' to b' to t to b channel. It is also fair to assume that the ratio of masses between one kind of undiscovered quark and the next heavier one would be at least a factor of two, with a jump from one generation to the next of the same type being at least a factor of four. Thus, a b' quark by this reasoning would be at least 346 GeV and a t' quark by this reasoning would be at least 692 GeV. Experiments are not so sensitive yet, and these are just minimums. If the top to bottom quark mass ratio is any indication, the b' and t' could easily have masses of several TeV or more. Also, any decay of a t' or b' would like a lot like a high energy top quark decay, differing only by a couple of "invisible" neutrinos and a couple of charged leptons from an ordinary top quark decay, and the charged leptons would most likely have the same tau prime generation and opposite charges making their annihilation before detection in a t' decay a very plausible possibility. A t' decay might be almost indistinguishable from a top quark decay in terms of observable end products; the ratio of missing energy to observable end products might be the only really distinctive signature of this decay.

Realistically, the fourth generation charged lepton ought to be the easiest to detect. Charged particles are much easier to find than electrically neutral ones, and a tau prime ought to be lighter than either at t' or a b'. The current experimental lower limit on a tau prime mass is about 100 GeV, but if the tau prime neutrino is more than half of the W mass, as experimental evidence demands that it must be, it would take a decay with about 150 GeV to unveil a tau prime neutrino and if the mass was a bit more than that, one would need a top quark decay of a very high energy top quark to produce one. Thus, the ratio of tau prime to tau mass is not less than about 65:1, if there is a tau prime. This is within the range of generation to generation mass gaps seen in the particles for which masses are currently known, but at the high end of those ratios, although a very heavy tau prime neutrino could damp that a bit.

It isn't clear to me how much LHC will be able to expand LEP boundaries in charged lepton detection, if at all, and if so, when.

Also worth pondering is the question of whether, even if there are fundamental particles yet to be discovered, if we have discovered all reasonably stable particles (e.g. all fundamental particles or composite particles longer lived than a muon).

The faster than hadronization decay of the top quark and of a hypothetical t' and b' and the lack of hadronization of leptons, also means that even if we haven't discovered every possible generation of fundamental particle, that we may have discovered (or theorized with great certainty even if we have not observed) every possible composite particle (with the possible exception of the glueball, which has been theorized but not directly observed and would have a mass on the order of about 300 GeV).

A new stable particle changes to makeup of the universe greatly and has all sorts of practical applications. For example, a stable sterile neutrino could be a dark matter candidate.

But, a t', b', tau prime, tau prime neutrino, W' or Z' that is at least as emphemeral as a top quark and is only created for that very brief moment in the most unnatural of high energy environments may have almost no relevance other than shedding light on the nature of the deeper theory that underlies the Standard Model thereby allowing for more precise theoretical determination of what are currently experimentally derived constants than is possible now (or explaining the innards of exotic astronomical objects like neutron stars and quasars).

For that matter, while the existence and mass of a neutral scalar Standard Model Higgs boson would have some very important implications for the technical aspects of the Standard Model at high energies, but any light Standard Model Higgs boson that isn't ruled out by experiment already would be ephemeral, and would have have few meaningful consequences for physics applications that I can discern.

We understand that world of particles with an electrical charge with such precision that it is almost unthinkable that there exists an electrically charged stable particle out there that hasn't been discovered. So, it is very unlikely that there is a stable quark or stable charged lepton or stable weak force boson out there that hasn't been discovered, or that there is another carrier boson for the electromagentic force in addition to the photon.

One could imagine a stable particle that lacks an electromagnetic charge that hasn't been discovered. Indeed, there are quite a few plausible hypothetical proposals for particles that fit that description such as a heavy sterile neutrino, right handed neutrinos, the lightest supersymmetric particles, a stable neutral Higgs boson, and the graviton. All of the fermions and massive bosons fitting that description would be dark matter candidates.

We can't rules out a stable particle with color charge (IIRC, however, even glueballs are not stable) but no electromagnetic charge with as much confidence, but also have no real strong theoretical reason to expect that one might be out there.

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