Anomalous scaling of strong interactions at low energies

The discovery of scaling in the high energy scattering of hadrons was a crucial step in understanding strong interactions. Hadrons behave at high energies as if they are composed of point like, almost free constituents. The explanation of this phenomenon based on the asymptotic freedom of Yang-Mills theories is one of the triumphs of quantum field theory. The low energy behaviour of strong interactions is far less understood theoretically and there is no systematic way to obtain the low energy scattering amplitudes from QCD because there are no reliable non-perturbative methods in four dimensional quantum field theory. Strong interactions at low energies are described by an approximate theory, the nonlinear sigma model. 12 refs