  In quantum field theory, the photon-fermion vertex can be described in terms
of four form factors which encode the static electromagnetic properties of the
particle, namely its charge, magnetic dipole moment, electric dipole moment,
and anapole moment. For Majorana fermions, only the anapole moment can be
nonzero, a consequence of the fact that these particles are their own
antiparticles. Using the framework of quantum field theory, we perform a
scattering calculation which probes the anapole moment with a spinless charged
particle. In the limit of low-momentum transfer, we confirm that the anapole
can be classically likened to a point-like toroidal solenoid whose magnetic
field is confined to the origin. Such a toroidal current distribution can be
used to demonstrate the Aharonov-Bohm effect. We find that, in the
non-relativistic limit, our scattering cross section agrees with a quantum
mechanical computation of the cross section for a spinless current scattered by
an infinitesimally thin toroidal solenoid. Our presentation is geared toward
advanced undergraduate or beginning graduate students. This work serves as an
introduction to the anapole moment and also provides an example of how one can
develop an understanding of a particle's electromagnetic properties in quantum
field theory.
