The chiral confining Lagrangian, based on 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 it takes into account an infinite number of transitions from meson-meson to quark-antiquark states. Starting from known $q\overline{q}$ poles, the transition coefficients ensure the strong shift of the poles for $\pi \pi$ and a much smaller shift for the $K\overline{K}$ systems. The resulting amplitudes $f_{\pi \pi }$ and $f_{K\overline{K}}$ are calculated in terms of $q\overline{q}$ and the free meson Green’s functions. Taking the $\pi \pi /K\overline{K}$ channel coupling into account, 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 $E=980\mathrm{MeV}$, 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.

• Received 16 October 2019
• Accepted 14 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.094028

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society