Single-spectral forms for three-point functions: The general-mass situation

Abstract

The establishment of spectral forms in source theory has been systematically studied, with it being a natural consequence of the causal methods employed therein that these results apply only for limited ranges of the particle masses. Here the three-point-function single-spectral form, considered in lowest nontrivial order and for scalar particles, is extrapolated to completely general values of the masses. The arguments employed continue in the physically oriented vein of source theory, not being founded on analyticity, and some consistency checks on these methods are included. In the case of stable particles the common spectral form with anomalous threshold is obtained, while for unstable particles the spectral mass squared can assume negative or complex values and the spectral weight function can take on an imaginary part. All the results are summarized in tabular form.