Abstract
In this work we study the spectral functions of scalar mesons in one- and two-channel cases by using nonlocal interaction Lagrangian(s). When the propagators satisfy the K\"allen-Lehman representation, a normalized spectral function is obtained, allowing one to take into account finite-width effects in the evaluation of decay rates. In the one-channel case, suitable to the light $\ensuremath{\sigma}$ and $k$ mesons, the spectral function can deviate consistently from a Breit-Wigner shape. In the two-channel case with one subthreshold channel, the evaluated spectral function is well approximated by a Flatt\'e distribution; when applying the study to the ${a}_{0}(980)$ and ${f}_{0}(980)$ mesons, the tree-level forbidden KK decay is analyzed.
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