A strategy for B-physics observables in the continuum limit

In a somewhat forgotten paper [1] it was shown how to perform interpolations between relativistic and static computations in order to obtain results for heavy-light observables for masses from, say, mcharm to mbottom. All quantities are first continuum extrapolated and then interpolated in 1/mₕ=1/mheavy. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small ambottom. We discuss how this strategy is extended to semi-leptonic form factors and other quantities of phenomenological interest. The essential point is to form quantities where the limit mₕ→∞ is approached with power corrections O(1/mₕ) only. Perturbative corrections ~αₛ(mₕ)γ+n are cancelled in the construction of the observables. We also point out how such an approach can help to control systematics in semi-leptonic decays with just large volume data. First numerical results with Nf = 2 + 1 and lattice spacings down to 0.039 fm are presented in [2].