One loop calculations on the Wess-Zumino-Witten anomalous functional at finite temperature

Abstract

We analyze the finite temperature (T) extension of the Wess-Zumino- Witten functional, discussed in a previous work, to one loop in chiral perturbation theory. As a phenomenological application, we calculate finite temperature corrections to the amplitude of the $π^0$ decay into two photons. This calculation is performed in three limits : i)$T/M_π<<1$, ii)the chiral limit at finite T and iii)$T/M_π>>1$ ($M_π$ being the pion mass). The $T$-corrections tend to vanish in the chiral limit, where only the kaon contribution remains (although it is exponentially suppressed).