🚀 go-pugleaf

In article <1992Sep13.175046.4015@ida.liu.se>, jonwa@ida.liu.se (Jonas Wallgren) writes...
>An article in the April 1983 issue of Scientific American gives a description
>of some models of quarks and leptons as composed of smaller particles. Two
>models presented are the preons from 1974 and the quite beautiful rishons from
>1979.
> 
>What has happend since then? Are there any new models? Are the old models
>refined or discarded? How does this problem relate to the current data
>indicating exactly 3 families of particles? How do the models fit together with
>W, Z, Higgs, ...?

Rule # 1:  There are *always* new models.

But there is also absolutely zero evidence for any quark or lepton substructure 
at the current time.  And that's not for lack of looking.  

Here's the way it works, qualitatively.  Assume that every quark and/or lepton
is actually made of a bound state of two or more "prequarks".  These prequarks
are bound by some new interaction between them.  Two quarks or leptons brought
near one another should then experience a force due to the interaction of
the prequarks in one quark with the prequarks in the other.  This results in 
an interaction which can be described mathematically as an effective four
quark or four-lepton interaction.  I.e, a (non-renormalizable) Feynman diagram
like this:

q2i       q2f
  \      /
   \    /
    \  /
     \/
     /\
    /  \
   /    \
  /      \
q1i       q1f

The strength of the coupling at the vertex depends on the details of the 
interaction and the compositeness scale L (it's usually written as Lambda,
which I can't type.) At energies much below L, the interaction is suppressed,
by inverse powers of L (1/L^2 for the lowest order contact interaction which 
I described above.)

Experimentalists have looked for four-fermion interactions beyond what
is predicted by the SM and used the null results to set limits on L for 
various classes of interactions between quarks and leptons.  The
Particle Data Book gives a variety of L's for different combinations, 
with typical values in the ballpark of L > 1 to 4 TeV.

Another consequence of substructure would be excited quarks or leptons, usually
denoted q* or l*.  Once a quark has constituents, you can imagine that like
a hydrogen atom, it should be possible to put in some energy and raise the
eigenstate of the subcomponents to 2S, 2P, etc., increasing the mass of the
quark and producing a new object, q*.  People have looked for such creatures,
with no sucess.  But mass limits have been set.  These values are typically
about 45 GeV, which (no accident) is roughly half of the Z mass. People
sometimes quote higher limits, which in general depend on more restrictive
assumptions about coupling constants (i.e., they are more model dependent.) 

So, as is typical in such speculative work, there is no evidence for
anything yet, but people continue to push the edge of the envelope, restricting
the possibilities by diligent searches.   This forces the theorists to (slowly)
modify their theories to predict new phenomena only where they may still exist
in spite of failed experimental searches, and, on rare occasion, eliminating
some theories outright.  

Rule # 2: There are always at least 5 new models to take the place of each 
one which is definitely ruled out.

-Scott
--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver