Anomalous processes at high temperature and density in a 2-dimensional linear $σ$ model

Details Anomalous processes at high temperature and density in a 2-dimensional linear $σ$ model Anomalous processes at high temperature and density in a 2-dimensional linear $σ$ model

2000-02-25

arxiv.org/abs/hep-ph/0002270v1

Phys.Rev. D63 (2001) 016001

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages Latex document, 2 postscript figures

Scientific paper

10.1103/PhysRevD.63.016001

We use the 2-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 tell that the $\pi^o\to\gamma$ amplitude should vanish if $m\to 0$, but we show that this conclusion is spoiled by infrared singularities. 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 $\pi^o\sigma\to\gamma$ and show that it does not vanish in the same limit.

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