THE CORRECT RENORMALIZATION OF THE GLUON OPERATOR IN A COVARIANT GAUGE

We give a correct prescription for the renormalization of composite operators containing gauge fields only. Using this procedure we are able to solve the long outstanding discrepancy which exists between the axial and covariant gauge calculations of the second-order anomalous dimension of the gluon operator. This discrepancy is due to an incorrect treatment of the mixing between gauge invariant (GI) and gauge variant (GV) operators in the literature. Contrary to what is usually claimed we show that in the general covariant-gauge radiative corrections to GV operators leads to counterterms corresponding to GI operators, which therefore contribute to the renormalization of the latter. Only if these counterterms are taken into account does the anomalous dimension of the gluon operator agree with the one obtained in the literature by choosing the axial gauge.