  Essential to QCD applications of the operator product expansion, etc., is a
knowledge of those operators that mix with gauge-invariant operators. A
standard theorem asserts that the renormalization matrix is triangular:
Gauge-invariant operators have `alien' gauge-variant operators among their
counterterms, but, with a suitably chosen basis, the necessary alien operators
have only themselves as counterterms. Moreover, the alien operators are
supposed to vanish in physical matrix elements. A recent calculation by Hamberg
and van Neerven apparently contradicts these results. By explicit calculations
with the energy-momentum tensor, we show that the problems arise because of
subtle infra-red singularities that appear when gluonic matrix elements are
taken on-shell at zero momentum transfer.
  Keywords: twist-two covariant gluon operator, finite part, mixing,
non-abelian, anomalous dimension, Ward identity, BRST, modified LSZ reduction,
Dixon, Taylor, Joglekar, Lee.
