A strategy for B-physics observables in the continuum limit

Conigli, Alessandro; Kuberski, Simon; Fritzsch, Patrick; Herdoiza, Gregorio; Frison, Julien; Heitger, Jochen; Sommer, Rainer; Simma, Hubert; Pena, Carlos; Gérardin, Antoine

Preprint

PUBDB-2023-07493

A strategy for B-physics observables in the continuum limit

Conigli, A. ; Frison, J.DESY* ; Fritzsch, P. ; Gérardin, A. ; Heitger, J. ; Herdoiza, G. ; Kuberski, S. ; Pena, C. ; Simma, H.DESY* ; Sommer, R. (Corresponding author)DESY*

2023

[10.3204/PUBDB-2023-07493]

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Report No.: DESY-23-216; HU-EP-23/71; MS-TP-23-53; arXiv:2312.09811

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].

Keyword(s): perturbation theory: correction ; lattice ; charm ; quark: mass ; continuum limit ; form factor ; numerical calculations ; finite size