Low-lying even parity meson resonances and spin-flavor symmetry revisited

Abstract

We review and extend the model derived in Garcia-Recio et al. [Phys. Rev. D 83, 016007 (2011)] to address the dynamics of the low-lying even-parity meson resonances. This model is based on a coupled-channels spin-flavor extension of the chiral Weinberg-Tomozawa Lagrangian. This interaction is then used to study the $S$-wave meson-meson scattering involving members not only of the $\ensuremath{\pi}$ octet, but also of the $\ensuremath{\rho}$ nonet. In this work, we study in detail the structure of the SU(6)-symmetry-breaking contact terms that respect (or softly break) chiral symmetry. We derive the most general local (without involving derivatives) terms consistent with the chiral-symmetry-breaking pattern of QCD. After introducing sensible simplifications to reduce the large number of possible operators, we carry out a phenomenological discussion of the effects of these terms. We show how the inclusion of these pieces leads to an improvement of the description of the ${J}^{P}={2}^{+}$ sector, without spoiling the main features of the predictions obtained in the original model in the ${J}^{P}={0}^{+}$ and ${J}^{P}={1}^{+}$ sectors. In particular, we find a significantly better description of the ${I}^{G}({J}^{PC})={0}^{+}({2}^{++})$, ${1}^{\ensuremath{-}}({2}^{++})$ and the $I({J}^{P})=\frac{1}{2}({2}^{+})$ sectors, which correspond to the ${f}_{2}(1270)$, ${a}_{2}(1320)$, and ${K}_{2}^{*}(1430)$ quantum numbers, respectively.