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We present our strategy and first results for calculating B-physics observables on the lattice with a controlled continuum extrapolation by combining static and relativistic heavy quarks. Computations in large volumes below the scale of the bottom quark and in the static limit are combined with results for relativistic bottom quarks in physically small volumes. This allows us to trace the mass-dependence of the observables from the charm region up to the static limit and to obtain results for B-physics by interpolation.
We employ 2+1 flavors of O(a) improved Wilson quarks at five values of the lattice spacing down to 0.039 fm. Interpolations are performed in the continuum and thus independent of the lattice regularization.