$O(aα_s)$ matching coefficients for the $ΔB$=2 operators in the lattice static theory

Details $O(aα_s)$ matching coefficients for the $ΔB$=2 operators in the lattice static theory $O(aα_s)$ matching coefficients for the $ΔB$=2 operators in the lattice static theory

1998-12-07

arxiv.org/abs/hep-lat/9812007v2

Phys.Rev. D60 (1999) 034501

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, no figures, uses REVTeX; added references, corrected typos

Scientific paper

10.1103/PhysRevD.60.034501

We present the perturbative matching coefficient to $O(a\alpha_s)$ which relates the $\Delta B$=2 operator in the continuum to that of the lattice static theory, which is important in the accurate extraction of the continuum value of the $B_B$ from lattice simulations. The coefficients are obtained by the one-loop calculations in both of the continuum and lattice theory. We find that two new dimension seven operators appear at the $O(a\alpha_s)$ with the O(1) coefficients. We also discuss the possible cancellation of $O(a\alpha_s)$ correction in the ratio $B_B=<\bar{B}|\Op_L|B>/ ((8/3)(f_{B}M_{B})^2)$ qualitatively.

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