## Wednesday, December 7, 2011

### Generic Limits On Fundamental Particle Mass

The muon has a mean lifetime of about 10^-6 seconds. No other quark or charged lepton has a mean lifetime of more than about 10^-8 seconds, and the half life of a top quark is on the order of magnitude of 10^-25 seconds. W boson are slightly less long lived than top quarks at 3*10^-25 s, and Planck time is on the order of 5*10^-44 seconds. Thus, there is a nineteen order of magnitude difference in decay rate between the longest lived second generation particle, and the shortest lived quark. There is a similar nineteen order of magnitude gap between the top quark/W boson decay time and Planck time.

Generally speaking, the heavier a fundamental particle is, the faster it decays. A muon is about 0.1 GeV. A top quark is about 173 GeV. The implication is that it may be that no particle can have a mass much more than 1700 times the top quark mass (about 294 TeV) without having a decay time of less than Planck time.

One could also related the decay rates to particle generation and note that the nineteen order of magnitude gap is between the longest lived second generation particle and the shortest lived third generation particle. This wouldn't rule out a fourth generation of fermions, but would rule out a fifth generation of fermions.

It is also conceivable that the decay rate of the W boson, which is the means by which fundamental particles can decay, is an absolute limit upon particle decay rates, in which case the top quark is the heaviest possible particle.

Given that all know massive particles decay via the weak force, the mass limitation inferred from decay rates are quite model independent. This kind of reasoning should apply, for example to massive technifermions, massive supersymmetric particles, and hypothetical higher generation bosons.

Now, this isn't necessarily a very strong bound. Some of the models consistent with a lightest Higgs boson of 127 GeV estimate that many of the supersymmetric particles would have masses on the order of 30 TeV, although several would have masses of less than 1 TeV, and experimental bounds on supersymmetric particle are similar to those on next generation quarks discussed below (but under 1 TeV).

Another possible bound on fourth generation Standard Model particles is in the CKM and PMNS matrixes; the absence of detectable amplitudes for transitions to more than three generations suggests that fourth generation Standard Model particles would have to be much heavier than a top quark, and that the decay chain would likely be dominated by a single possibility as the top quark decay is dominated by the decays to bottom quarks.

As I've noted elsewhere, the absence of hadrons made of top quarks also implies, a fortiori, that hadrons made of fourth generation quarks would also not exist. More generally, unless a supersymmetric analog to the strong force had a much more rapid time frame than the Standard Model strong force, supersymmetric hadrons of anything but lowest generation supersymmetric particles would be ruled out, since all supersymmetric particles are heavier than a top quark.

Experimental Bounds on Fourth Generation Particles

Fourth generation quarks (conventionally labeled t' and b') are experimentally excluded for the b' below 199 Gev and for the t' below 256 GeV. These values are not updated for the latest 2011 LHC bounds, which put a lower bound on the b' mass of 385 GeV, and the puts a reasonably expected t' mass values, if there is a t' quark, higher.

If the t' to t quark mass ratio were similar to the t quark to c quark mass ratio, one would expect the t' quark to have a mass of 20 TeV; the b quark to s quark ratio would imply a t' quark mass of 7 Tev; the s quark to u quark mass ratio would imply a t' quark mass of about 3.5 Tev; the tau to muon mass ratio would imply a t' mass of about 3 TeV. The ratio of c quark mass to u quark mass, or of muon to electron mass would suggest an even greater t' mass. Of the b/c, c/s, and s/d mass ratios, none are smaller than a factor of about 3, so one would expect a b' mass of not less than about 522 GeV and much heavier masses on the order of 1 TeV or more would be plausible given expectations for the t' mass.

The lower experimental bound on a tau prime (i.e. fourth generation lepton) mass is about 100 GeV, which is about 55 times the tau mass, and d/s/b type mesons appear to tend to be within an order of magnitude of mass of their same generation charged lepton, so a mass in the high hundreds of GeV would not be particularly unexpected. We know that a Z boson can give rise to a top/antitop pair with a combined mass of 348 GeV which far exceeds the 90 GeV of the Z boson rest mass. But, perhaps at some point there is a limit, and if that limitation is less than the correct mass for fourth generation fermion if there was one, then that limit would prevent fourth generation fermions from arising. The conventional statement of the experimental limitation on fourth generation neutrino mass from precision electroweak measurements is 45 GeV.

Experimental bounds on Z' bosons are in the high hundreds of GeVs.