Uncertainties of hadronic scalar decay calculations

Dispersion relations---a corollary of unitarity and analyticity---are among the few methods which can be employed to study low energy processes in QCD. In this work we critically revisit the calculation of decay widths of a hypothetical light scalar boson into pions and kaons. Strong interactions of the mesons in the final state affect these decays significantly. We argue that applications of the dispersion relations to the calculation of these decay widths, which are present in the literature, rely on an uncontrollable approximation of the reduced S-matrix. When a limited number of initial and final decay channels are considered, in general neither a unitary S-matrix nor its version corrected by an inelasticity factor are justified. The scalar form factor calculation provides a transparent example to illustrate this statement. Therefore, the results of this calculation, which are important for theoretical, cosmological and experimental applications, must be treated with caution. Our work, therefore, calls for a breakthrough in the understanding of the dispersion relations of realistic many-channel systems.