Vector Meson Dominance, Axial Anomaly and the Thermal behavior of gρωπ(T)

By using a thermal Finite Energy QCD Sum Rule, we are able to establish the temperature dependence of the gωρπ(T) strong coupling. It turns out that this coupling decreases as a function of temperature, vanishing at the critical temperature. This corresponds to a possible deconfining phenomenological signal. This result, together with the Vector Meson Dominance (VMD) expression for the amplitude π 0 → γγ, allows us to establish that this amplitude also vanishes at the critical temperature, in agreement with previous independent analysis. This results supports, once again, the validity of VMD at finite temperature. Several posssible scenarios are discussed. However, if VMD would not hold at finite temperature, then we will not be able to find a prediction for the thermal behavior of the π 0 → γγ amplitude. The discussion of the thermal behavior of hadronic Green functions has called the attention of many authors during the last years, due to their relevance in the diagnosis of the Quark-Gluon Plasma (QGP) [1]. Several correlators have been discussed in the literature, using different techniques as, for example, QCD (thermal) Sum Rules and different expansions in the frame of effective low energy hadronic lagrangians. Among the interesting results, it is worthwhile to mention here that the imaginary part of all hadronic Green's functions grows with temperature. For a two point Green function, this means that the hadronic width is an increasing function with temperature. See [2] and [3]. This important result has been confirmed through many independent analysis. On the other side, it seems that there is no such consensus about the temperature dependence of hadronic masses. Pisarski, for example, [4] has argued that if Vector Meson Dominance (VMD) is valid at finite temperature, then M ρ (T c) > M ρ (0), being T c the critical chiral symmetry restoration temperature. Note that T c should coincide with the critical deconfining temperature T d , or if not, both temperatures should be quite similar, T d T c. If VMD breaks down there is no prediction for the behavior of M ρ (T). For T < T c different models can give opposite answers. Compare, for example, [2] and [5]. The validity of VMD at finite temperature turns out to have a strong impact on the physics related to the QGP, justifying a careful analysis of this subject from different perspectives. In a previous work, we have shown that …