CarlB said:
While I believe this to be the case, I thought that the standard belief is that the quark potential energy rises linearly with distance and that this explains confinement. I've seen the graphs from the lattice QCD people showing this comes out in simulation, for example. Can you explain further?
In lattice calculations, you take two static quarks and calculate the gluon field created by these sources. In the real world, when one "tries to take two quarks appart", at some point the glue tube breaks into meson/antimeson pair in the real world. First, let me remind two scales :
Size of hardons : 1 fm
Compton wavelength of light quarks : 40 fm
Now at which scale does the string break ? At first, one can evaluate it from the static quark/antiquark potential. If you take the string breaking to occur when the potential energy exceeds twice the pion mass, you'll get something around 0.5 fm ! I also wanted to quote lattice simulations of the string breaking, but they
must use heavy quarks. Even when you overcome difficulties with light quarks, they'll give you something around 1.2 fm (see for instance
Observation of String Breaking in QCD). In any case, we are very far from the quark Compton wavelength. The conclusion one can draw from this is that confinement must be
quantum mechanical. We cannot use classical pictures.
This argument might appear weak. There are more sound ones. Very convining to me is the following paper :
Instantons and baryon dynamics
Once one-gluon exchange and linear "confining" potential are smoothed out, u and d correlations in the nucleon are still calculable by the instanton contribution only. Instantons are intrinsically quantum mechanical. Although they are calculated as classical solitons in the euclidean gluon field, they correspond to quantum tunneling in the minkovskian gluon field (like a
WKB approximation).
Yet other arguments exist. I will not try to sum up agruments from "Is the proton really bound ?" at page 11 of
QCD Phenomenology. The section is about one page long.
I have long been fascinated by Gribov's views on physics in general, and on quark confinement in particular. It is actually in his work that I first read that
the problem of confinement is with
light quarks.
Gribov program of understanding confinement
QCD at large and short distances (annotated version)
CarlB said:
Do you recall the old theory that supposed that the bare quarks were heavier than the nucleons, but that their binding energy was comparable to their rest masses?
I have already heard about this, but never read details.