Anomalous processes at high temperature and density in a two-dimensional linear σ model -: art. no. 016001

We use the two-dimensional sigma model as a toy model to study the behavior of anomalous amplitudes in the limit where the constituent quark mass is small. Symmetry arguments show that the pi (0) --> gamma amplitude should vanish if m --> 0, but we show that the one-loop pi (0) gamma amplitude does not satisfy this property because of infrared singularities. However, when a proper regularization (resummation of a thermal mass, for instance) is taken into account, this amplitude vanishes as expected. We also study the amplitude pi (0) sigma --> gamma and show that it does not vanish in the same limit.