PoS - Proceedings of Science
Volume 453 - The 40th International Symposium on Lattice Field Theory (LATTICE2023) - Quark and Lepton Flavor Physics
A strategy for B-physics observables in the continuum limit
R. Sommer*, A. Conigli, J. Frison, P. Fritzsch, A. Gérardin, J. Heitger, G. Herdoiza, S. Kuberski, C. Pena and H. Simma
Full text: pdf
Pre-published on: May 07, 2024
Published on: November 06, 2024
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, $m_{\rm charm}$ to $m_{\rm bottom}$.
All quantities are first continuum extrapolated and then interpolated in $1/m_h=1/m_{\rm heavy}$. Large volume computations are combined with
finite volume ones where a relativistic bottom quark is accessible with small $am_{\rm bottom}$.
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].
DOI: https://doi.org/10.22323/1.453.0268
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