Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1992-08-05
Phys.Rev.D47:1206-1218,1993
Physics
High Energy Physics
High Energy Physics - Lattice
27 pages, 2 figures (Plain TeX, figures in an appended postscript file)
Scientific paper
10.1103/PhysRevD.47.1206
The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.
Boucaud Ph.
Leroy J.-P.
Micheli J.
Pene Olivier
Rossi G. C.
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