Electromagnetic Form Factors of the Nucleon

TLDR

Electromagnetic form factors are constrained by gauge invariance, with weak gauge invariance following from Lorentz covariance and providing no new functional constraints, whereas strong gauge invariance imposes stricter conditions via the generalized Ward identity. The study investigates how strong gauge invariance restricts the current operator and influences the calculation of nucleon form factors, particularly the charge and magnetic moments expressed through F1 and F2. Using a covariant generalization of the fixed‑source static model that reproduces the static limit as M→∞, the authors calculate the second moment of the charge distribution via neutron‑electron interaction and provide a consistent framework for recoil corrections. Strong gauge invariance necessitates line currents that substantially affect form factors, notably increasing the proton charge radius even in the static approximation, implying that large‑mass intermediate states contribute significantly, and the resulting recoil corrections are found to be large.

Abstract

The physical interpretation of the electromagnetic form factors is discussed with special reference to the gauge invariance of particular theories. A distinction is made between the condition that the one nucleon matrix element satisfy the equation of continuity ("weak gauge invariance") and the stronger condition imposed by the generalized Ward identity ("strong gauge invariance"). The former is shown to be a consequence of covariance under the improper Lorentz transformations, and hence it has no new content concerning the functional behavior of the form factors. The latter implies restrictions on the current operator which may have an important effect on the results of calculations of form factors.In connection with the physical interpretation, it is noted that the moments of the charge and current distribution are determined by ${F}_{\mathrm{eh}}={F}_{1}\ensuremath{-}(\frac{{q}^{2}}{2M}){F}_{2}$ and ${F}_{\mathrm{mag}}=(\frac{1}{2M}){F}_{1}+{F}_{2}$. Specifically the second moment of the charge distribution, $\ensuremath{-}6{{F}_{\mathrm{ch}}}^{\ensuremath{'}}(0)$, is found, in the case of the neutron, to be directly measured by the neutron-electron interaction without the intervening subtraction of the Foldy term.These matters are investigated in detail by means of a specific model of the nucleon which is a covariant generalization of the fixed source static model having the property that it gives results identical with the static model in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$. It is found that strong gauge invariance requires the addition of line currents which make significant contributions to the form factors in general and, in particular, to the proton charge radius even in the static approximation. This suggests that as a consequence of strong gauge invariance, important contributions to the charge radius must arise in any theory from intermediate states of large mass. The model also provides a means of consistently calculating recoil corrections to the static model. They are found to be large.