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 $\pi$ octet, but also of the $\rho$ 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 $I^G(J^{PC})=0^{+}(2^{++})$, $1^{-}(2^{++})$ 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.

• Received 26 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.096006