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As a general rule of thumb, massive particles (both composite and fundamental) tend to decay rapidly through the weak force, while less massive particles tend to be more stable. Hence, taus are shorter lived than muons, top quarks are shorter lived than charm quarks, and all mesons and baryons except protons and neutrons are highly unstable. My understanding is that this relationship is largely captured in the Standard Model electro-weak equations.

Are there any notable cases where the decay rate and the mass of the particle appear experimentally to deviate from the expected relationship?

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an interesting extension to your question - shouldn't we expect there to be islands of stability for hadron spectra? i'm referring to the analogy with heavy nuclei –  lurscher Mar 16 '11 at 20:03
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Dear Andrew, first, I edited your "anomoly" which should be "anomaly". I couldn't watch it.

Second, all the decays you mention use the weak force and the elementary Feynman diagram is always the same: it's a cubic vertex with one W-boson, one decaying fermion, and one fermionic decay product. So the amplitude is essentially $g_{SU(2)} \bar u_{final} \gamma_\mu u_{initial} \epsilon_W^\mu$.

However, what hugely depends on the mass of the fermions are the kinematic factors - the Lorentz-invariant phase space, if you wish. The "universal" amplitude above has to be integrated over all allowed momenta of the final particles, with the $d^3 p / 2E$ measure. Also, there's $1/2E$ for each initial particle.

The most impressive "failure of dimensional analysis" among these weak decays is the decay rate of the ordinary neutron - its half-life is ten minutes! That's an extremely long time scale, especially if you compare it to the half-life of top quark etc. that you mentioned. Both decays are driven by the same elementary process whose Lorentz-invariant amplitude is essentially identical! The neutron is this stable because it's just slightly heavier than the proton, the main decay product, and the phase space for the allowed electron's and antineutrino's momenta in the final state is just extremely small. (There are probably other similarly long half-lives of unstable nuclei that decay via beta-decay - which are just heavier counterparts of the decaying neutron. The neutron decay is also a simple case of a beta-decay.)

There exists no observed disagreement between any weak decay (of a known particle) and the Standard Model prediction. That's a glimpse of a much more general fact: the Standard Model just universally works. If I am the first one who tells you that it does, it's unfortunate.

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Thanks you for your analysis. Of course, while you state "the Standard Model just universally works," this is neither definitively confirmed in all cases experimentally (e.g. observed CP violations in excess of Standard Model predictions that may not be random), nor do you, a vocal advocate of SUSY, believe that Standard Model "just universally works" as currently formulated. I agree that it is extremely accurate, but am curious if there might be significant unexplained experimental deviation that could be beyond the Standard Model in decay rates (unlike the neutron that the SM explains). –  user2592 Mar 16 '11 at 20:33
    
No, Andrew, you're wrong. When I say that the Standard Model works, it does mean that all particles ever observed obey it, and in particular, all particles whose lifetime was measured agree with the theoretical predictions of the lifetime - within the theory+experimental error. That's true for failures of the Standard Model that ultimately occur because of SUSY and other new physics - none of them has been measured as of March 17th, 2011. Again, no, there are no unexplained decay rates. Haven't I written it clearly? Be sure that any such anomalies would be stunning and known to everyone. –  Luboš Motl Mar 17 '11 at 7:21
    
Lubos... Frankly both of your understanding is far beyond mine, which is why I'm wondering if you have seen this story, and whether it changes your viewpoint on the issue? projectworldawareness.com/2010/10/… I'm in the process of investigating it further to determine if its hogwash, partially true, commonly known, or something we should be concerned/excited about. I'd appreciate some expert input. –  user3345 Apr 30 '11 at 0:36
    
@DCJerboa: don't take my word for it, but at first glance the page you linked to (at least the material at the top about solar neutrinos and the nuclear decay rate) seems completely bogus. –  David Z May 3 '11 at 17:28
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