Axial anomaly, vector meson dominance and $π^0 \to γγ$ at finite temperature

Abstract

A thermal Finite Energy QCD Sum Rule is used to determine the temperature behaviour of the $ωρπ$ 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 $π^0 \to γγ$ amplitude, which is also found to vanish at the critical temperature, as expected. This result supports the validity of VMD at $T \neq 0$. However, if VMD would not hold at finite temperature, then there is no prediction for the $π^0 \to γγ$ amplitude.