epsilon -meson coupling constants and scale invariance breaking

A general method for obtaining ratios of coupling constants (defined by pole residues) in a way which is completely free of resonance /background separation troubles is devised and applied to the epsilon -meson. Huge discrepancies between previous determinations are shown to arise (i) from inherent ambiguities in the methods used, (ii) from lack of knowledge about the epsilon -pole position and (iii) from the well-known up-down ambiguity in the isospin-0 s-wave pi pi phase shift delta /sub 0//sup o/. Taking as input pi N phase shifts, available information on delta /sup 0//sub 0/ and including all possible uncertainties, the authors find for down-up or up-up delta /sup 0//sub 0/: g/sub epsilon NN//g/sub epsilon pi pi /=(6+or-3) mu /sup -1/, and for down-down or up-up delta /sup 0//sub 0/: g/sub epsilon NN//g/sub epsilon pi pi /=(1.8+or-0.5) mu /sup -1/ The precise validity of the scale invariance breaking prediction (g/sub epsilon NN//g/sub epsilon pi pi /). m/sup 2//sub epsilon //2M=1 is fulfilled in some theoretical pi pi models having Gamma /sub epsilon / approximately=m/sub epsilon / approximately=500 MeV and delta /sup 0//sub 0/ of up-down type, but is excluded if sigma /sup 0//sub 0/ is down-up or up-up. (15 refs).