Limits on coupling constants in field theories with finite sources

Abstract

The interaction of a boson field with a source is assumed to vanish outside of a radiusa; no special properties are assumed for this source within the radius. It is shown that with such a model for the interaction of pions or K-mesons with nucleons and hyperons, rigorous upper limits, depending only upona and the particle masses, can be established for the renormalized coupling constantsg2Λ,g2pΣκ,g2pΛκ corresponding to the matrix elements for the processes π+Λ0↔Σ.\(\bar K\)+p↔Σ and K-+p↔Λ0 For the pion-nucleon interaction a maximumg2npπ is found, above which there must exist a doubly charged state of the system π++p. Ifg2npπ approach infinity or ifa approaches zero, it is proved that the neutron-proton mass difference goes to zero independently of other interactions or whether the bare masses are identical. Similar results hold for the mass difference of any baryon pair if they transform into each other by single boson emission or absorption. Finally a general class of field theory models, which will always have « ghosts », is described.