  We compute the leading probability for a gluon to flip helicity state upon
traversing a background plane wave gauge field in pure Yang-Mills theory and
QCD, with an arbitrary number of colours and flavours. This is a one-loop
calculation in perturbative gauge theory around the gluonic plane wave
background, which is treated without approximation (i.e., to all orders in the
coupling). We introduce a background-dressed version of the spinor helicity
formalism and use it to obtain simple formulae for the flip amplitude with pure
external gluon polarizations. We also give in-depth examples for gauge group
SU(2), and evaluate both the high- and low-energy limits. Throughout, we
compare and contrast with the calculation of photon helicity flip in
strong-field QED.
