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

Abstract

We analyze the finite temperature (T) extension of the WessZumino -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 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).

Temperature dependence of the anomalous effective action of fermions in two and four dimensions

“…It is also noteworthy that, according to [28], the vanishing of the pionic decay amplitude in the chirally symmetric phase will presumably be recovered when quantum pionic fluctuations are properly taken into account since they regulate the infrared sector. Another set of calculations of anomalous (and non anomalous) mesonic amplitudes should be mentioned here [29,[23][24][25]. They correspond to the low temperature limit and thus well within the phase were chiral symmetry is broken.…”

Neutral pion decay in dense Skyrmion matter

“…However, as shown in the previous works on the other properties of pion [1,3], after the resummation they lead only a minor corrections compared to the zeroth order values that are nothing but those obtained in the mean field approximation. Temperature effects could have been revealed, for example, in [11] from the pion loops, because the pion propagator at finite temperature differs from that at zero temperature by discrete Matsubara frequencies. One may extract a density dependence by evaluating similar pion loops by using the modified pion propagator with effective pion mass.…”

“…on temperature has been investigated by various authors [8][9][10][11]. It is well understood that though the anomaly, which drives the decay, is temperature independent, nonetheless the amplitude does depend on T through the phase space or through the modification of the thermal quark propagators in evaluating explicitly the triangle diagram.…”

“…It is well understood that though the anomaly, which drives the decay, is temperature independent, nonetheless the amplitude does depend on T through the phase space or through the modification of the thermal quark propagators in evaluating explicitly the triangle diagram. In particular, [10,11] consider temperature effects in the Wess-ZuminoWitten (WZW) effective Lagrangian which incorporates the anomaly. The coefficient of the anomalous term corresponding to 0 !…”

Another look at charge fractionalization at finite temperature

“…This connection between the chiral anomaly and the induced fractional fermion number raise the question: How can the chiral Jacobian and hence the chiral anomaly be temperature independent [15][16][17][18][19][20][21][22][23] while the fractional fermion number is affected by temperature [24][25][26][27]? This question is very much like the problem of how the amplitude for π 0 → γγ, which is deeply related to the chiral anomaly, is affected by temperature in the face of the temperature independence of the coefficient of the chiral anomaly [28][29][30][31][32][33][34]. Here, we present a study of this question.…”