Low Energy Hadron Physics

Ask a group of particle theorists about low energy hadron physics and they will say that this is a subject that belongs to the age of the dinosaurs. However, it is GeV physics that controls the outcome of every hadronic interaction at almost every energy. Confinement of quarks and gluons (and any other super-constituents) means that it is the femto-universe that determines what experiments detect. What we still have to learn at the start of the 21st century is discussed. 1 Low energy dynamics Low energy hadron dynamics is determined by the structure of the QCD vacuum. Once we thought this ground state was empty, but now we know it is a seething cauldron of quarks, antiquarks and gluons. Indeed, so strong are their interactions that they form all measure of condensates: qq, GG, qGq, etc. It is the nature of this vacuum and the scale of these condensates that determine low energy hadron physics. It is this that we can learn about at DAΦNE. Most importantly, the vacuum determines the spectrum of hadrons and its scale. Thus the nucleon has a mass of 1 GeV, while conventional qq mesons, like the ρ, are two-thirds of this mass, but pions merely 140 MeV. Indeed, it is these masses squared that determines dynamics and having m2π = 0.02 GeV 2 makes pions by far the lightest of all hadrons. But why? This is a question for which we have had a good idea of the answer for many decades, but in fact its only now that we are on the threshold of definitively testing. We begin with QCD with two flavours of quark, for simplicity. Then we have kinetic energy and interaction terms in the Lagrangian for both the up quark and the down. Since the proton and neutron masses are almost equal, we can imagine that mu = md. Then QCD has an exact SU(2)F symmetry, which is reflected at the hadron level by the proton and neutron having the same strong interactions. Now, the scale of QCD is fixed