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 non-linear 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 point like 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.

Scalar glueball, scalar quarkonia, and their mixing

“…• The radiative decay φ → a 0 (980)γ, which cannot proceed if a 0 (980) is a qq state, can be nicely described in the kaon loop mechanism [24]. This suggests a considerable admixture of the KK component.…”

On modeling the scalar meson dynamics with RChT

“…Various models (e.g. [6,7]) have been proposed to describe these decays. In our previous consideration [9] we performed the separate fits (π 0 π 0 and πη) for the mass-parameters of scalar mesons and the angle θ , while 4c d c m = F 2 and c d = c m relations of Ref.…”

Radiative ϕ decays with derivative interactions

“…We thus intend to continue the analysis initiated in Ref. [14] about derivative interactions by studying the decay mechanism a.1 in both the f 0 and the a 0 channels in relation to radiative φ decays. We aim to do it by properly taking into account loops and finite-width effects using the formalism developed in Ref.…”

“…The latter coupling can again occur in two ways: via derivative coupling (mechanism b.1, proportional to c f0KK , see Ref. [14]) or via non derivative coupling (mechanism b.2, proportional to d f0KK , see Ref. [2,16,17]).…”

“…A first study of derivative interactions (thus setting d f0ππ = d f0KK = 0) has been performed in Ref. [14], where it has been shown by using Breit-Wigner propagators for the scalars that derivative couplings describe the data better than non-derivative ones. A detailed study involving non-derivative interactions only (setting c f0ππ = c f0KK = 0) has been performed in Ref.…”