Axial anomaly, vector meson dominance and ${\pi }^0\to \gamma \gamma$ at finite temperature

Abstract

A thermal Finite Energy QCD Sum Rule is used to determine the temperature behaviour of the $\omega \rho \pi$ strong coupling. This coupling decreases with increasing $T$ and vanishes at the critical temperature, a likely signal for quark deconfinement. This is then used in the Vector Meson Dominance (VMD) expression for the ${\pi }^0\to \gamma \gamma$ amplitude, which is also found to vanish at the critical temperature, as expected. This result supports the validity of VMD at $T\ne 0$. However, if VMD would not hold at finite temperature, then there is no prediction for the ${\pi }^0\to \gamma \gamma$ amplitude.

8 pages, no figures

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