Approximate Bounds on Coupling Constants from Analyticity, Crossing, and Unitarity

Abstract

If the exchange forces in a unitary scattering amplitude are too large, there is a breakdown of analyticity due to the appearance of ghosts. As an illustration of this, the condition that the singlet amplitudes of nucleon-nucleon scattering have no ghosts is formulated as a simple eigenvalue problem for the bound on the pion-nucleon coupling constant, in the approximation of neglecting all but one-pion-exchange terms. It is found that the pion-nucleon coupling constant $g$ could not be more than 2\textonehalf{} times its actual value without producing a ghost. It is suggested that the most stringent bounds should come from a consideration of the Pomeranchuk pole. It is further speculated that the electromagnetic and weak interactions may eventually be bounded in a similar way.