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We present the perturbative matching coefficient to $O(a\alpha_s)$ whichrelates the $\Delta B$=2 operator in the continuum to that of the latticestatic theory, which is important in the accurate extraction of the continuumvalue of the $B_B$ from lattice simulations. The coefficients are obtained bythe one-loop calculations in both of the continuum and lattice theory. We findthat two new dimension seven operators appear at the $O(a\alpha_s)$ with theO(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.Comment: 14 pages, no figures, uses REVTeX; added references, corrected typo

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:math>matching coefficients for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>operators in the lattice …

O(aαs)matching coefficients for theΔB=2operators in the lattice …