A non-perturbative chiral approach for meson-meson interactions

Abstract

A non-perturbative method [1] which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe meson-meson interactions up to √s<_~1.2 GeV, extending in this way the range of applicability of the information contained in Chiral Perturbation Theory (X PT) [2], since this perturbative series is typically restricted to √s<_500 MeV. The approach uses the O(p²) and O(p^4) Lagrangians. The seven free parameters resulting from the O(p^4) Lagrangian are fitted to the experimental data. The approach makes use of the expansion of T^(-1) instead of the amplitude itself as done in X PT. The former expansion is suggested by analogy with the effective range approximation in Quantum Mechanics and it appears to be very useful. The results, in fact, are in good agreement with a vast amount of experimental analyses [3,4].
The amplitudes develop poles corresponding to the fₒ(980), aₒ(980), ρ(770), K*(890), the octet contribution to the φ , fₒ(400 −1200) ≡ σ and κ [4]. The total and partial decay widths of the resonances are also well reproduced.