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.