Scalar mesons in the chiral theory with quark degrees of freedom

Abstract

The Chiral Confining Lagrangian, based on the chiral theory with quark degrees of freedom, is used to study the spectroscopy of scalar mesons. The formalism does not contain arbitrary fitting parameters and takes into account infinite number of transitions from meson-meson to quark-antiquark states. Starting from known $q\bar{q}$ poles the transition coefficients ensure the strong shift of the poles for the $\pi \pi$ and much smaller shift for the $K\bar{K}$ systems. The resulting amplitudes $f_{\pi \pi }$ and $f_{K\bar{K}}$ are calculated in terms of the $q\bar{q}$ and the free meson Green's functions. With the account of the $\pi \pi /K\bar{K}$ channel coupling one obtains two resonances: a wide resonance $E_1$ in the range 500-700 MeV and narrow $E_2$ near 1 GeV, which can be associated with $f_0(500)$ and $f_0(980)$. A similar analysis, applied to the $I=1$ channel, shows that in this case two very close poles in different sheets appear near $E=980$ MeV, which can be associated with the $a_0(980)$ resonance. The obtained $\pi \pi$ interaction amplitudes, $\mathrm{Re}{f}_{\pi \pi }(E)$ and $\mathrm{Im}{f}_{\pi \pi }(E)$ are compared with the known data.

Comments: v5: 29 pages, 6 figures; version accepted to PRD, new equations with explanations are added, several important insertions are made, the list of references is correspondingly enlarged