2-LOOP CALCULATION OF THE ANOMALOUS DIMENSIONS OF 4-FERMION OPERATORS WITH STATIC HEAVY QUARKS

We compute in the heavy-quark effective theory the two-loop anomalous dimension of the effective four-fermion operator OBAR(DELTAB=2) whose matrix element determines the B-parameter of the B-meson. Dimensional reduction is the regularization method chosen in this calculation, which is performed using the techniques already developed by us to treat the two-loop renormalization in standard dimensional regularization of the heavy-quark axial current. For N = 3, we find gamma(OBAR)DELTAB=2(2) = -1/36[202 + 26xi(2) - 16n(F)], with xi(2) = 1/6pi2. This anomalous dimension turns out to be equal to the one in standard dimensional regularization. We employ gamma(OBAR)DELTAB=2(2) to derive the complete scheme-independent order alpha(s) correction to the relation between O(DELTAB=2) in QCD and its counterpart OBAR(DELTAB=2) in the effective theory. For the heavy-quark axial current, we recalculate the corresponding analogous order-alpha(s) relation in dimensional reduction and the 't Hooft-Veltman dimensional regularization scheme. We show explicitly that this is renormalization-scheme independent, which completes the study carried out by us in our previous work. Moreover, these relations are used to obtain the renormalization constants for the lattice values of the B-meson decay constant, f(B), and B-parameter, B(B), whose product enters the theoretical prediction of the B0-BBAR0 mixing. As an extra result, the theoretic subtleties of dimensional reduction applied to the heavy-quark effective theory are exposed and resolved.