Extraction of bare Form Factors for ${\mathrm{B}}_{\mathrm{s}}\to \mathrm{K}\ell \nu$ Decays in non-perturbative HQET

Abstract

We discuss the extraction of the ground state $⟨\mathrm{K}(\mathbf{p})|V_{\mu }(0)|\mathrm{B}(0)⟩$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings $0.075,0.05$ fm and pion masses $330,270$ MeV are used from the O($a$)- improved CLS 2-flavour simulations and the final state momentum is $|\mathbf{p}|=0.5\mathrm{GeV}$. The b-quark is treated in HQET including the $1/m_{\mathrm{b}}$ corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is $not$ limited by the $1/m_{\mathrm{b}}$ corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

Comments: 38 pages, 23 figures