6533b82afe1ef96bd128ca15

RESEARCH PRODUCT

Isovector and isoscalar meson cloud contributions to the nucleon electromagnetic form factors

subject

description

We have calculated the nucleon form factors ${G}_{E,M}^{(p,n)}{(q}^{2})$ in the linear \ensuremath{\sigma} model to one-meson-loop order plus (two-loop) $\ensuremath{\gamma}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$ anomaly. The previously derived $\ensuremath{\gamma}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$ anomaly generally reduces the nucleon radii and produces a shift of the magnetic moments of order 0.1 ${\ensuremath{\mu}}_{N}$ or less. We present analytical results for ${G}_{E,M}^{p,n}(0)$ which display explicitly their dependence on hadron masses and coupling constants. Analytical results for the radii are also given and the chiral singularities they contain $(\mathrm{ln}{m}_{\ensuremath{\pi}}$ and ${m}_{\ensuremath{\pi}}^{\ensuremath{-}1})$ are exposed. These come from the $\ensuremath{\pi}\ensuremath{\pi}$ intermediate state contribution to the form factors and not from the chiral quark substructure of nucleons or mesons. The leading chiral singularity has a universal strength while the chiral log (next-to-leading singularity) picks up a model (or approximation) dependence in terms of ${g}_{A}$ and the threshold behavior of the $\ensuremath{\pi}N$ amplitude ${A}^{(\ensuremath{-})}(\ensuremath{\nu},0)$. The chiral singularities appear only in the isovector nucleon radii $〈{r}_{1,2}^{2}{〉}^{I=1}$, the leading ${m}_{\ensuremath{\pi}}^{\ensuremath{-}1}$ term appears only in $〈{r}_{2}^{2}{〉}^{I=1}$ due to a peculiar cancellation between two independent form factor combinations ${\ensuremath{\Gamma}}_{1,3}{(q}^{2})$. The isoscalar anomaly $\ensuremath{\gamma}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$ is finite for ${m}_{\ensuremath{\pi}}\ensuremath{\rightarrow}0$.