Compositeness Limits -- Have We Reached Rock Bottom?

[lpetrich]

Particle Data Group - 2017 Review has some strong lower limits for the mass scales of possible quark and lepton compositeness, or at least the compositeness of the easier-to-study ones, like up and down quarks and also electrons. The limits are well into the TeV range, though they are somewhat model-dependent.

This means that electrons, up quarks, and down quarks do not start to disintegrate even after applying energies a million times their rest masses.

Here are the maximum ratios of disintegration energy to rest mass for entities previously discovered to have been composite:

• Atoms: 10^(-8) (ionization of hydrogen atoms)
• Nuclei: 10^(-3) (dissociation of deuterons)
• Hadrons: 1 (deep inelastic scattering off of nucleons)

That makes it very difficult for Standard-Model elementary fermions to be composite: they are much less massive than their compositeness energy scales.

But there is a theoretical analogy: light mesons, like pions. Their mass is roughly sqrt(mq*mc) where mq is the quarks' average mass and mc = QCD energy scale. For mq << mc, m(meson) << mc also. So if the electron has a compositeness scale of about 1 TeV, then the electron's constituents would have to have masses around 1 eV.

 

[Vanadium 50]

Pions are special because they are goldstones. That means there is an inexact symmetry that is driving their masses near zero. (If the symmetry were exact, they would be massless)

 

[lpetrich]

Pions are special because they are goldstones. That means there is an inexact symmetry that is driving their masses near zero. (If the symmetry were exact, they would be massless)

So in the scenario that I'd mentioned, the Standard Model's leptons and quarks are all pseudo-Goldstone particles, like the pion.

 

[Vanadium 50]

That's starting to sound like a personal theory. So far as I know, this is impossible without supersymmetry and virtually impossible with it.

 

[lpetrich]

That's starting to sound like a personal theory. So far as I know, this is impossible without supersymmetry and virtually impossible with it.

Looks like that mechanism cannot work. So it'll be very hard for electrons and up and down quarks to be composite.