RENORMALIZATION-GROUP ASPECTS OF ETA'-]GAMMA-GAMMA

The theoretical issues involved in the calculation of the decay amplitude-eta' --> gamma-gamma are discussed, with particular emphasis on the renormalisation group (RG) aspects. In contradiction to the existing literature, it is shown that the straightforward generalisation of the well-known PCAC formula for pi-0 --> gamma-gamma to eta' --> gamma-gamma is inconsistent with the RG, and therefore incorrect in principle. The decay amplitude for eta' --> gamma-gamma is found to involve a new decay constant F, defined in terms of the two-point Green function of the composite operator iq-gamma-5qBAR, which is both RG invariant and process independent, and a proper vertex, describing the coupling of the "glue" component of the eta' to photons, which is not constrained by the anomalous Ward identities for spontaneously broken chiral symmetry. The phenomenological implications of this result are discussed.