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

We estimate the radiative corrections of order α/π 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 δκ_p = -3.42 × 10^-3 and δκ_n = 1.34 × 10^-3. We also study the effects from photon loops with internal Δ(1232) isobars. For two customary versions of the ΔNγ vertex and spin-3/2 propagator, these radiative corrections have values of δκ_p^(Δ) = (-0.9, 0.0) × 10^-3 and δκ_n^(Δ) = (-1.2, 0.8) × 10^-3, respectively. Taking these ranges as a systematic error, our estimates read δκ_p = (-3.9 ± 0.4) × 10^-3 and δκ_n = (-1.5 ± 1.0) × 10^-3.