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

Abstract

The anomalous dimensions of four-quark operators $({\bar{q}}_i{q}_j{)}_{V-A}({\bar{q}}_k{q}_l{)}_{V-A}$ are calculated in the large $N_f$ 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.

Comments: 17 pages, LaTex, two figures