On the spectral functions of scalar mesons

Understand

In this work we study the spectral functions of scalar mesons in one- and two-channel cases.

• When the propagators satisfy the K\"allen-Lehman representation a normalized spectral function is obtained, allowing to take into account finite-width effects in the evaluation of decay rates.
• In the one-channel case, suitable to the light 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 Flatte' distribution; when applying the study to the a_0(980) and f_0(980) mesons the tree-level forbidden KK decay is analysed.