Too much mass from confinement

[bcrowell]

This month's Scientific American has an article about preons, which are hypothetical particles that the standard-model particles would be built out of. They discuss a problem with confinement in these models. We know that, say, an electron has a size less than x. This requires an uncertainty in momentum of at least h/x. Say for simplicity that the preon is ultrarelativistic. Then its energy has to be at least h/x (in units with c=1), and this is equivalent to a rest mass of at least h/x. Putting in x<~10^-17 m for an electron gives m>~10^-25 kg, which is much too big for an electron. All of these arguments would seem to apply equally well to any theory in which standard-models have substructure. E.g., it would seem to apply to string theory.

How is this not a showstopper for such models? The Sci Am article makes vague references to a resolution by some technical trick. The same problem occurs for a pi meson, and they say this was solved by Goldstone 1961 for bosons. Apparently 't Hooft extended the solution to fermions in 1979.

Can anyone explain what's going on, using crayons?

 

[tom.stoer]

First of all you are right, confinement of preons as substructures should result in large masses.

The trick for the pion is that it is the Goldstone boson for the (nearly exact) chiral symmetry (with nearly massless quarks); the corrections to m_π = 0 are due to the small quark masses m_q. You can see how this trick fails when considering the η' meson. The η' is the would-be goldstone boson of the axial U(1). But this symmetry is not broken spontaneously but by to the axial anomaly - and therefore the rather large mass of the η' can be explained.

The problem with the confinement mass does not apply to string theory b/c here the elementary particles do not have a stringy substructure but they are identitcal with the string. And the calculations of the string ground states show that there are massless excitations in the spectrum (string theory has a moch more severe problem to explain the tiny masses of the elementary particles).

I do neither know how 't Hooft solved the problems for fermions, nor do I know how to construct a preon model which has exactly the right global symmetry from which the known particles could arise as Goldstoen bosons and how to deform or break this symmtry such that the particles become massive.

 

[MathematicalPhysicist]

We can always invite t' Hooft to PF to explain himself, I believe he was seen once at stackexchange.

 

[Vanadium 50]

Confinement of preons in generally makes a mess. What we would like to see is a preon theory explain flavor: i.e. the mu and tau are somehow excited states of the electron. The problem is that you need to make the preons heavy to explain their non-observation, which means you need to make their potential well deep. e.g. a preon weighs 5 TeV + m_e, and two preons are bound together by 10 TeV, so the final object weighs m_e. This fine-tuning may or may not be explained by a symmetry principle.

Now you are running into a problem harder to run away from. The binding potential needs to be very deep and very short-range, otherwise we would have seen evidence by now. This potential looks a lot like a delta-function, and as every student of QM knows, a delta function has exactly one bound state. So you now can't use preons to solve the problem you wanted them to in the first place.