On the spectral functions of scalar mesons

TL;DR

This paper investigates the spectral functions of scalar mesons, demonstrating how they deviate from simple models and can be accurately described using the K"allen-Lehman representation and Flatte' distribution, with implications for decay rate calculations.

Contribution

It provides a detailed analysis of scalar meson spectral functions in one- and two-channel cases, including finite-width effects and decay channel influences.

Findings

Spectral functions can deviate from Breit-Wigner shapes in the one-channel case.

Two-channel spectral functions with a subthreshold channel are well approximated by Flatte' distribution.

Analysis of a_0(980) and f_0(980) mesons reveals the impact of forbidden KK decay channels.

Abstract

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.