Scalars and pseudoscalars in nonlinear chiral dynamics

Abstract

A chiral-U(3)×U(3)-invariant Lagrangian and a (3*,3) + (3,3*) breaking term are written in terms of (3*,3) + (3,3*) representations which are functions of nonlinearly transforming scalar and pseudoscalar fields. The invariant Lagrangian admits only derivative couplings between scalar and pseudoscalar fields. The kinetic-energy SU(3) breaking which is induced by the scalar vacuum expectation values leads to a simple parametrization of the pseudoscalar mixing angle. Estimates of the ${\eta }^{\prime }\to \gamma \gamma$ and $\eta \to \gamma \gamma$ amplitudes and the $\frac{(\psi \to {\eta }^{\prime }\gamma )}{(\psi \to \eta \gamma )}$ ratio compare reasonably well with experimental values. Scalar-particle decays are discussed, and the $\delta \mathrm{}\left(980\right)\mathrm{}\to \eta \pi$ width determines $\frac{F_K}{F_{\pi }}\simeq 1.15$. The $\kappa \mathrm{}\left(1350\right)\mathrm{}$ and $\epsilon \mathrm{}\left(1300\right)\mathrm{}$ widths are estimated and the ${\eta }^{\prime }\to \eta \pi \pi$ decay discussed. The overall description compares well with experiment.