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We determine a basis of dimension-7 operators which arise at O($a$) in theSymanzik expansion of the $\Delta B=2$ operators with static heavy quarks. Weconsider both Wilson-like and Ginsparg-Wilson light quarks. Exact chiralsymmetry reduces the number of these O($a$) counterterms by a factor of two.Only a subset of these operators has previously appeared in the literature. Wethen extend the analysis to the O($1/m$) operators contributing beyond thestatic approximation.

Renormalization of HQET $\Delta B=2$ operators: O($a$) improvement and $1/m$ matching with QCD