Two-loop calculation of the anomalous dimensions of four-fermion operators with static heavy quarks
1993; Elsevier BV; Volume: 401; Issue: 1-2 Linguagem: Inglês
10.1016/0550-3213(93)90300-e
ISSN1873-1562
Autores Tópico(s)Black Holes and Theoretical Physics
ResumoWe compute in the heavy-quark effective theory the two-loop anomalous dimension of the effective four-fermion operator OΔB = 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 γOΔB = 2(2) = −136[202+26ξ(2)−16nF], with ξ(2) = 16π2. This anomalous dimension turns out to be equal to the one in standard dimensional regularization. We employ γOΔB = 2(2) to derive the complete scheme-independent order αs correction to therelation between OΔB = 2 in QCD and its counterpart OΔB = 2 in the effective theory. For the heavy-quark axial current, we recalculate the corresponding analogous order-αs 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, ƒB, and B-parameter, BB, whose product enters the theoretical prediction of the B0−B0 mixing. As an extra result, the theoretic subtleties of dimensional reduction applied to the heavy-quark effective theory are exposed and resolved.
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