Could second and third generation SM particles NOT be fundamental?

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Main Question or Discussion Point

could second and third generation SM particles NOT be fundamental?

since they are unstable and rapidly decay, could second and third generation SM particles NOT be fundamental? perhaps as bound states of more fundamental first generation particles?

if they are not fundamental, then do we have to worry about SUSY partners of these?
 

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  • #2
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Very, very, very, very unlikely. Their decay happens because it can, and it happens faster for more massive particles because there are more possible momenta that the resulting particles can have.

You can ask "How can that be possible, since momentum is a continuous quantity and not a discrete one"? The answer is that the possible momenta will be discrete for a finite volume, and that there are thus more possible momenta if the total energy is large.

With a large enough volume, the sums become integrals, making the calculation somewhat easier. The volume also drops out of the final results for decay rates and cross sections.

One can also use dimensional analysis to estimate the behavior of decay rates. If a particle's decays involve highly-relativistic and/or massless particles, then the most significant mass scale will be the parent particle's mass. Since in quantum mechanics with hbar = c = 1, mass, momentum, and energy have units of reciprocal length and time, the decay rate will be proportional to the particle's mass.

Violation of these conditions can lead to much greater dependence on mass. Weak interactions, for m << mW, give

m5/v4

m = particle's mass, v = Higgs vacuum expectation value
 
  • #4
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Furthermore, there isn't any evidence of such compositeness.

Figure 41.6 in Plots of cross sections and related quantities (rev.) at the Particle Data Group site shows how well electron-positron collision rates agree with the Standard Model.
Can't there be a bound state that also agrees electron-positron collision rates agree with the Standard Model? Or could second/third generation be a quantized excited version of first generation, etc?
 

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