Hybrid Renormalization of Penguins and Dimension-5 Heavy-Light Operators

We discuss the renormalization of local, scalar and pseudoscalar dimens= ion-5 operators containing a heavy and a light quark field at scales below the heavy-quark mass, using the formalism of the heavy-quark effective theory (HQET). We calculate the anomalous dimensions of these operators and thei= r mixing to one-loop order. We also perform the one-loop matching of gluon = and photon penguin operators onto operators of the HQET. We discuss applicati= ons of our results to the mixing of gluon and photon penguin operators at low renormalization scales, and to the calculation of $1/m_Q^2$ corrections t= o meson decays constants.