Resonances from meson-meson scattering in U(3) CHPT

TL;DR

This paper performs a comprehensive one-loop calculation of meson-meson scattering in U(3) chiral perturbation theory with explicit resonances, analyzing resonance properties and their N_C behavior, including the ext{sigma} resonance.

Contribution

It introduces the first complete one-loop unitarized meson-meson scattering analysis within U(3) chiral perturbation theory with explicit resonances, including N_C dependence.

Findings

Vector resonances follow standard quark-antiquark trajectories.

Scalar resonances like f_0(1370) and a_0(1450) tend to a scalar octet at large N_C.

The ext{sigma} resonance exhibits a distinct N_C behavior.

Abstract

In this work, the complete one loop calculation of meson-meson scattering amplitudes within U(3)\otimes U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a non-perturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their N_C behaviors. The resulting N_C dependence is the first one in the literature that takes into account the fact that the \eta_1 becomes the ninth Goldstone boson in the chiral limit for large N_C. Within this scheme the vector resonances studied, \rho(770), K^*(892) and \phi(1020), follow an N_C trajectory in agreement with their standard \bar{q}q interpretation. The scalars f_0(1370), a_0(1450) and K^*(1430) also have for large N_C a \bar{q}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4 GeV. The f_0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1 GeV. The \sigma, \kappa and a_0(980) scalar resonances have a very different N_C behavior. The case of the \sigma resonance is analyzed with special detail.