Hadrons, quarks, and all that

In his comment, Inam asked the very sensible question "what makes people believe that quarks are point like particles when all they can observe is the hadronic state of quarks?". The answer is that although we detect only hadrons (which we think consist of confined quarks) in detectors, the way, for instance, high-energy electrons scatter from a proton, is very well described by a picture in which the electrons are scattering from three point-like objects (of charges +2/3, +2/3, and -1/3) within the proton. This discovery was made in experiments done at the Stanford Linear Accelerator in the 1960s, and won the Nobel Prize in 1990.

More generally, although at long distances quarks are not observed as free particles, quarks are 'asymptotically free' and so in any experiment that achieves high enough energies we can compute the outcome of the experiment using the fundamental theory of the strong interaction, QCD. In QCD the quarks are point-like, and the statement in Dr Cardman's talk was just that all experiments to date are consistent with that assumption, and no evidence for non-point-likeness has yet been seen. Note that there is a nice feature of QCD here: to look for non-point-like-ness (=composite-ness) of quarks you have to use a very-high-energy accelerator, so you can probe very short distances. But at very short distances quarks are almost free, so you can calculate the "standard QCD" effects (i.e. assuming point-like quarks) using perturbation theory. Bounds are then obtained by adding extra terms to the QCD Lagrangian and seeing what they would do to the data. (Summary of results available here.)

Inam's other question, about quark-hadron duality, is a little harder to answer. At its most basic level this is just a statement that a complete set of states with quark degrees of freedom and a complete set of states with hadron degrees of freedom are both, well, a complete set of states. So you can do the quantum mechanics using whichever basis you prefer. BUT you may find that things that are easy to describe in one basis are difficult to describe in another. I believe, although I am not sure, that similar phenomena occur in Condensed Matter systems (e.g. bases of 'fundamental' degrees of freedom or quasi-particles). The standard statement of duality is encapsulated in a 'folk theorem' due to Steven Weinberg: 'You can use whatever degrees of freedom you want to describe the system, but some choices will be more efficient than others'. (My paraphrase, since I couldn't find the original source.)

More specifically, Jefferson Lab has done some very nice experiments on a really interesting phenomenon called "local duality" which is a statement about averages of electron-scattering observables in which hadronic resonances are seen being equal to the result for the same observable if you compute it with quarks in the limit of very high energies where that description is more efficient.