New Rigorous Bounds on Coupling Constants in Field Theory

Abstract

We improve the rigorous upper bound derived by $\mathrm{L}$ukaszuk and Martin for the ${\ensuremath{\pi}}^{0}\ensuremath{-}{\ensuremath{\pi}}^{0}$ scattering amplitude at the symmetric point. Our principal new tool is the "parametric dispersion relation" of Auberson and Khuri. Also, for a ${\ensuremath{\varphi}}^{4}$ field theory with a scalar bound state, we establish an upper bound on the physical coupling constant to the bound state as a function of its mass. Numerican examples of this bound are given for several bound-state masses.