Abstract
We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the continuum limit can be taken with confidence. The resulting precision is of interest for extractions of $V_{\rm ub}$. The size of the corrections of order $1/m_{\rm b}$ is just estimated at present but it is expected that their inclusion does not pose significant difficulties.
Highlights
Weak decays of B-mesons are a very important piece in the puzzle of understanding about how well the Standard Model of particle physics describes Nature
ALPHA Collaboration / Physics Letters B 757 (2016) 473–479 b) renormalize the currents and, if an effective theory is used, relate them to QCD (“matching”), c) take their continuum limit, d) extrapolate to the quark masses realized in Nature, e) map out the q2 dependence
While we focused our effort on taking the continuum limit of non-perturbatively renormalized matrix elements at a fixed Kaon momentum, we have so far neglected the dependence on the light-quark mass which – according to [6,7] – is below our errors
Summary
ALPHA Collaboration / Physics Letters B 757 (2016) 473–479 b) renormalize the currents (and matrix elements) and, if an effective theory is used, relate them to QCD (“matching”), c) take their continuum limit, d) extrapolate to the quark masses realized in Nature, e) map out the q2 dependence. We consider a single value of the momentum transfer and a single value of the light dynamical quark masses with only two degenerate dynamical flavors These restrictions mean that our computation does not immediately advance phenomenology, but since a continuum limit was not taken before we can see for the first time how it works, and the result provides a cross check on the uncertainty estimates of previous computations. Given that the inclusion of 1/mb effects in the systematic treatment of HQET [12] was not a severe problem (apart from a lot of work) in other quantities [13,14,15] we are very encouraged to complete the started programme towards phenomenologically relevant results
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