Radiative corrections to the magnetic moments of the proton and the neutron

Abstract

We estimate the radiative corrections of order $\alpha /\pi$ to the magnetic moments of the proton and the neutron. The photon-loop diagram of the vertex-correction type is evaluated with phenomenological nucleon vector form factors. Infrared-finiteness and gauge-invariance require the inclusion of the wave-function renormalization factor from the self-energy diagram. Using recent empirical form factor parametrizations the corrections amount to $\delta {\kappa }_p=-3.42\cdot 10^{-3}$ and $\delta {\kappa }_n=1.34\cdot 10^{-3}$. We study also the effects from photon-loops with internal $\Delta (1232)$-isobars. For two customary versions of the $\Delta N\gamma$-vertex and spin-3/2 propagator, these radiative corrections have values of $\delta {\kappa }_p^{(\Delta )}=(-0.9,0.0)\cdot 10^{-3}$ and $\delta {\kappa }_n^{(\Delta )}=(1.2,-0.8)\cdot 10^{-3}$, respectively.

Comments: 15 pages, 8 figures, 3 tables