Light Scalar Mesons in the Improved Ladder Approximation of QCD with Strong $U_A(1)$ Breaking

Abstract

The spectrum and the mixing angle of the light scalar nonet mesons are studied using the extended Nambu-Jona-Lasinio (NJL) model as well as the improved ladder approximation (ILA) of QCD with U_A(1) symmetry breaking interaction. The U_A(1) breaking is represented by the Kobayashi-Maskawa-'t Hooft (KMT) interaction. The strength of the KMT interaction in the NJL model is determined so as to reproduce the electromagnetic decays of the \eta meson. That in the ILA approach is determined so as to reproduce the pseudoscalar meson spectrum. In the extended NJL model, we study the qualitative features of the scalar meson spectrum. In the scalar nonet spectrum, the KMT interaction is found to give the right ordering of \sigma - a_0 masses and a few hundred MeV mass difference between the \sigma and a_0 mesons. We also find that the strangeness content in the \sigma meson is about 15%. In the ILA approach, we confirm the qualitative features of the results from the extended NJL. We obtain the mass spectra of the light pseudoscalar nonet mesons and the \sigma, a_0 mesons which are consistent with current experimental data. On the other hand, we show that the obtained f_0 and K_0^* state can not be identified directly with the experimental data. It may suggest that the f_0(980) and \kappa(700-900) states may not be explained only by the quark-anti quark state. We also find that the strangeness content in the \sigma meson is about 5%. We obtain the result that the U_A(1) breaking interaction reproducing the mass spectrum of the pseudoscalar meson gives large effects on the scalar meson mass spectrum.