Chiral approach to phi radiative decays

Abstract

The radiative decays of the phi meson are known to be a good source of information about the ${a}_{0}(980)$ and ${f}_{0}(980)$ scalar mesons. We discuss these decays starting from a nonlinear model Lagrangian which maintains the (broken) chiral symmetry for the pseudoscalar (P), scalar (S) and vector (V) nonets involved. The characteristic feature is derivative coupling for the SPP interaction. In an initial approximation which models all the scalar nonet radiative processes together with the help of a pointlike vertex, it is noted that the derivative coupling prevents the ${a}_{0}$ and ${f}_{0}$ resonance peaks from getting washed out (by falling phase space). However, the shapes of the invariant two final PP mass distributions do not agree well with the experimental ones. For improving the situation we verify that inclusion of the charged $K$ meson loop diagrams in the model does reproduce the experimental spectrum shapes in the resonance region. The derivative coupling introduces quadratic as well as logarithmic divergences in this calculation. Using dimensional regularization we show in detail that these divergences actually cancel out among the four diagrams, as expected from gauge invariance. We point out the features which are expected to be important for further work on this model and for learning more about the puzzling scalar mesons.