Anomalous dimensions of four-quark operators in the large N_f limit

The anomalous dimensions of four-quark operators $(\bar q_i q_j){V-A} (\bar q_k q_l){V-A}$arecalculatedinthelarge$N_f$ limit. As expected, the result is a convergent series without renormalon ambiguities. Using the approximation of “Naive Nonabelianization”, an additional all-order contribution to the anomalous dimension matrix is obtained which is somewhat larger than the exact NLO correction itself. Possible phenomenological applications in nonleptonic B decays and $B^0-{\bar{B}}^0$ mixing are briefly considered.