Are we there yet?

Jefferson Lab was built largely to probe the "transition region": that domain of energies and momentum transfers where a description of nuclei in terms of protons and neutrons gives way to a description based on the fundamental QCD degrees of freedom of quarks and gluons.

At very large energies we know that the interactions of quarks and gluons can be computed in perturbation theory (pQCD: perturbative Quantum Chromodynmics). This allowed theorists to predict (already in the 1970s) how various quantities that JLab has now measured should behave in the limit of large energies/momentum transfer. The only problem is that no-one really knew how large was lareg. Some of these predictions have been borne out, e.g. those for the disintegration of a deuteron by a high-energy photon. But, for the most part, the "asymptotic region", where these predictions based on pQCD become correct, has proven elusive. JLab appears to be stuck in a transition region covers more kinematic territory than many originally thought.

One observable for which pQCD makes a definite prediction is the "form factor" of a pion. This function encodes how different the pion's charge distribution is from the charge distribution of a point particle. (Yes, you guessed it, the charge distribution of a point particle is that all the charge is at a single point.) The form factor can be accessed via electron-pion scattering experiments. But it is very very difficult to build a target out of pions. (Yes, that was me exercising my gift for understatement.) So experimentalists have cleverly figured out how to get at the pion form factor in experiments where the pion is "electro-produced" in the interaction of a beam of electrons with a proton target. It turns out that protons (and neutrons for that matter too) fluctuate into a pion-nucleon state in ways that are governed by quantum mechanics (think Heisenberg Uncertainty Principle). So if you come in with an electron and hit the pion in that "virtual state" you can knock it away from the proton and detect it in a detector. Look at that: you scattered an electron from a pion target! Pion form factor here we come!

But the problem is that there are a bunch of other mechanisms by which pions can be produced when the electron-proton interaction takes place. So the experimentalists, such as Dr Gaskell who gave Monday's talk, need a model of these other processes in order to isolate the piece of the reaction they are interested in: the piece where the electron interacts with the pion in that pion-nucleon virtual state. With such a model in hand they can subtract off the other stuff and extract numbers for the pion form factor at a variety of momentum transfers where they have measured the pion electro-production process.

The results they get are intriguing, if vaguely disappointing. They show that the pion form factor is behaving with the power of momentum transfer predicted by pQCD (should go like 1/Q^2). But the pre-factor is off by a factor of a few. In astronomy a prediction of the right power law and a coefficient within an order of magnitude would be a success. However, in this case it has been the cause of some head-scratching by theorists, who have built a variety of different models to try and understand the additional processes (i.e. processes beyond those predicted by pQCD) that are taking place in the regime probed by the JLab experiments. Some of these models suggest that data on the pion form factor taken at an upgraded, 12 GeV, JLab will show the beginnings of an approach to the pQCD pion form factor. But at best it seems that 12 GeV JLab will provide only a glimpse of the promised land where the quarks and gluons inside the pion play together under the benevolent rule of pQCD. So let me ask the question: will all this effort and experimental ingenuity have been worth it if what we get out of this program are some very nice measurements of the pion's form factor in the "transition region", i.e. at Q^2's where pQCD does not apply?