  Even though neutrinos are neutral particles and interact only via the
exchange of weak gauge bosons, charged leptons and quarks can mediate a
coupling to the photon field beyond tree level. Inside a relativistically
strong laser field nonlinear effects in the laser amplitude can play an
important role, as electrons and positrons interact nonperturbatively with the
coherent part of the photon field. Here, we calculate for the first time the
leading-order contribution to the axial-vector--vector current-coupling tensor
inside an arbitrary plane-wave laser field (which is taken into account exactly
by employing the Furry picture). The current-coupling tensor appears in the
calculation of various electroweak processes inside strong laser fields like
photon emission or trident electron-positron pair production by a neutrino.
Moreover, as we will see below, the axial-vector--vector current-coupling
tensor contains the Adler-Bell-Jackiw (ABJ) anomaly. This occurrence renders
the current-coupling tensor also interesting from a fundamental point of view,
as it is the simplest Feynman diagram in an external field featuring this kind
of anomaly.
