Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory

We perform a complete and systematic calculation of the octet-baryon form factors within the fully covariant approach of $SU(3)$ chiral perturbation theory at $\mathcal{O}(p^3)$. We use the extended on-mass shell renormalization scheme and include explicitly the vector mesons and the spin-$3/2$ decuplet intermediate states. Comparing these predictions with data including magnetic moments, charges, and magnetic radii, we determine the unknown low-energy constants and give predictions for yet unmeasured observables, such as the magnetic moment of the ${\mathrm{\Sigma }}^0$ and the charge and magnetic radii of the hyperons.

Figure 1

Tree-level diagram that contributes to the baryon form factors. The vertex runs through orders $\mathcal{O}(p^1)$ to $\mathcal{O}(p^3)$. The wavy and continuous lines correspond to photon and octet-baryon fields, respectively.

Figure 2

Loop diagrams that contribute to the baryon form factors up to $\mathcal{O}(p^3)$. The wavy, dashed, and single (double) continuous lines correspond to photon, pseudoscalar meson, and octet (decuplet) baryon fields, respectively. All the vertices are of the leading-order Lagrangians.

Figure 3

Diagram with vector-meson contributions to the baryon form factors. The wavy, double dashed, and continuous lines correspond to photon, vector meson, and octet-baryon fields, respectively.

Figure 4

Diagrams contributing to the proton self-energy with nucleon (a) and $\mathrm{\Delta }$ (b) loop contributions.