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arXiv · 1903.05870

Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQET

Felix Bahr·Debasish Banerjee·Fabio Bernardoni·Mateusz Koren·Hubert Simma·Rainer Sommer
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Abstract

We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_μ(0)|\mathrm{B} ({\bf 0})\rangle$ 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 $|{\bf p}|=0.5\,{\rm GeV}$. 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.

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Felix Bahr, Debasish Banerjee, Fabio Bernardoni, Mateusz Koren, Hubert Simma, Rainer Sommer. 2019-03-14. Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQET. https://doi.org/10.1142/s0217751x19501665

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