  Splitting functions govern the scale evolution of parton distribution
functions. Through a Mellin transformation, they are related to anomalous
dimensions of twist-two operators in the operator product expansion. We study
off-shell operator matrix element, where the physical operators mix under
renormalization with other gauge-variant operators of the same quantum numbers.
We devise a new method to systematically extract the Feynman rules resulting
from those operators without knowing the operators themselves. As a first
application of the new approach, we independently reproduce the well-known
three-loop singlet splitting functions obtained from computations of on-shell
quantities.
