A strategy for B-physics observables in the continuum limit

Abstract

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, $m_{\mathrm{charm}}$ to $m_{\mathrm{bottom}}$. All quantities are first continuum extrapolated and then interpolated in $1/m_h=1/m_{\mathrm{heavy}}$. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small $a{m}_{\mathrm{bottom}}$. 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 $m_h\to \infty$ is approached with power corrections O$(1/m_h)$ only. Perturbative corrections $\sim {\alpha }_s(m_h{)}^{\gamma +n}$ 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 $N_f=2+1$ and lattice spacings down to 0.039 fm are presented in [2].

Comments: Lattice 2023 talk