Uncertainties in tests of long-range charge independence

Abstract

It is pointed out that determinations of the pion-nucleon coupling constant g based on distant collisions in proton-proton (p-p) and neutron-proton (n-p) scattering employing pseudoscalar (ps) theory have questionable validity because the physical particles are not the idealized undressed particles to which the one-pion exchange (OPE) considerations really apply. Neither the pion-pion (π-π) interaction nor the electromagnetic form factors of nucleons (N) and the π's are explained by the derivation of the OPE interaction. Furthermore the Fermi-Yang pion model suggests directly the entrance of derivatives in the π-N interaction energy even though it had to be modified through the years. Although the literal applicability of the ps theory to the calculation of OPE effects is doubtful the exponential dependence of the equivalent OPE potential (OPEP) on the N-N separation is on the other hand a consequence of the tunneling phenomenon in the transfer of a π from one N to another, such as is present in the theory of nucleon-transfer reactions in low energy nuclear physics. The qualitative support for the mathematical form of the OPE from N-N scattering data is thus not a convincing argument for any one detailed mathematical form of OPE theory. It is pointed out that the presence of the factor ( m π/M) 2) in the OPE phase shift formula is of questionable validity. Estimates are made of the effect of disregarding the variation of the factor with m π. The estimates indicate that the π-N coupling constants derived from p-p and n-p data will agree appreciably better with each other as a result. This modification does not destroy the highly probable dependence of the OPE phase shifts on m π expected from the picture of π-tunneling through the region of negative kinetic energy between the nucleons. The modification is equivalent to the replacement of the ps coupling theory by the pv theory employing the factor ƒ/ m π in the interaction energy with actual values of m π corresponding to π +, π −, and π O . It is suggested that tests of long-range charge independence performed by comparing ( g 2) p- p with ( g 2) n- p do not emphasize sufficiently the rather likely possibility of differences in the coupling of the charged pions to both n and p as compared with that of the neutral pion. Possible uncertainties in the coupling constant determinations caused by the characteristics of experimental data are mentioned and briefly discussed. Different forms of the π-N interaction energy are considered. It is pointed out that there is no compelling reason for considering only local forms in necessarily phenomenological formulations of the theory, because the nucleon, pions, and other mesons involved (ϱ, η, μ, ϕ) are not definitely elementary particles and are coupled to each other. The limited meaning of charge independence of the π-N interaction without the incorporation of a quantitative explanation of the pion mass differences is emphasized. It is pointed out that the employment of the pv coupling theory made in this paper is consistent with relatively recent generalizations of that theory made by S. Weinberg and J. Schwinger in connection with PCAC, soft pion production, π-π interaction, nucleon magnetic moments, and related questions. The relationship of matters discussed to theories of electromagnetic mass differences is briefly considered.