Upper Limits for Coupling Constants in Field Theories

Abstract

Upper bounds to the magnitude of the coupling constant for the vertex $A+B\ensuremath{\leftrightarrow}C$ are explored for meson theories with spatially fixed sources and also for the full relativistic theory without approximation. Two types of limit are obtained which depend upon whether or not the vertex $A+\overline{B}\ensuremath{\leftrightarrow}D$ exists where $\overline{B}$ is the antiparticle to $B$ and $D$ is stable. Any greater value is inconsistent with unitarity and the mass spectrum of stable particles. In fixed-source theories the limits can be explicitly expressed in terms of simple properties of the given source function; in the nonapproximated relativistic theory they involve some knowledge of the number or position of the nodes of the single-partial wave absorptive amplitude on the nonphysical (left-hand) cut. When inelastic scattering of $A$ by $B$ is neglected and the mass of $C$ is only slightly less than the sum of the masses of $A$ and $B$, the upper bounds are equal to each other and to the coupling constant if $C$ is a pure bound state of $A$ and $B$.