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Are Standard-Model particles bound states?

  1. Jul 22, 2012 #1
    So far, we've discovered this compositeness hierarchy:
    Atoms - bound states of electrons, nuclei, photons
    Nuclei - bound states of nucleons and other hadrons
    Hadrons - bound states of quarks and gluons

    So are any Standard-Model particles bound states of any other particles?

    The compositeness searches described in the Particle Data Group's pages yield lower limits of a few TeV for 4-elementary-fermion interactions and lower limits from 100 GeV to a few TeV for excited leptons. More generally, work like [hep-ex/0001023] Standard Model Physics at LEP describes very good agreement up to about 100 GeV per particle for electron-positron collisions.

    This is about 200,000 times an electron's rest mass, and if electrons are bound states, one must somehow get cancellation at least as good as that. That is rather difficult to picture. For atoms, one gets relative binding energies around 10^(-8) - 10^(-5), for nuclei, around 0.01, and for hadrons, around 1. So for an electron to be a bound state, its relative binding energy must be at least 200,000. Has any model builder come up with a way for that to happen?
  2. jcsd
  3. Jul 23, 2012 #2


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    The sum of particle masses plus (negative) binding energy must be 511 keV. As particle masses are usually arbitrary in theory and the coupling strength can be arbitrary, too, I would expect that this is possible somehow. It looks a bit like fine-tuning, however.
  4. Jul 24, 2012 #3
    Rather extreme fine tuning - less than 1 part in 200,000.

    Binding energy = (energy of free particles) - (energy of bound state)

    If (mass of bound state) << (mass of free particles), then one gets the extreme cancellation that I'd mentioned.
    Last edited: Jul 24, 2012
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