Broken symmetries and bare coupling constants

Abstract

There are known cases of symmetry laws valid for one kind of interaction but broken by another. Each symmetry is then supposed to be exact for bare masses and coupling constants but only approximate for the renormalized quantities, like neutron and proton masses. We ask how the equality of unrenormalized constants can be rephrased as a statement about measurable quantities. This question is particularly important in connection with proposed strong-interaction symmetries that are supposed to be badly broken. The answer appears to involve the limits of ratios of experimental quantities at very high momenta. We discuss first the connection between wave-function renormalizations and weak and electromagnetic form factors. Then we take up the measurement of strong-interaction vertex renormalization factors by the study of scattering amplitudes at energies and momentum transfers large compared to all masses. The last part of the work is based in part on indications from the perturbation development of pseudoscalar meson theory, but we hope it will point the way to similar results in a better theory.