Soft photon production from real-time dynamics of jet fragmentation

Soft photons produced in heavy ion collisions are an important tool for probing the properties of the quark-gluon plasma. It is therefore crucial to understand the background - soft photons produced in elementary collisions. Low theorem states that soft photon production in hadron collisions is dominated by Bremsstrahlung off charged initial and final state hadrons. Surprisingly, almost every experiment observed an enhancement (by a factor of $2\div 5$) above Low theorem's prediction. This is the longstanding puzzle of "anomalous soft photon production." The phenomenon is not observed in processes with leptonic final states, which suggests that the mechanism is due to nonperturbative QCD evolution. We study this phenomenon using an exactly soluble, massless, Abelian model in $1+1$ dimensions which shares with QCD many important properties: confinement, chiral symmetry breaking, axial anomaly and $\theta$-vacuum. We then apply this model to the soft photon production in the fragmentation of jets produced in $Z^0$ decays and find a qualitative agreement with the data.