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

## TL;DR

This paper presents a non-perturbative lattice QCD method to extract form factors for B_s to K decays, emphasizing excited state removal and achieving about 2% precision, with future work needed on multi-hadron effects.

## Contribution

It introduces a lattice QCD approach using HQET with excited state suppression techniques to accurately determine B_s to K form factors.

## Key findings

- Achieved ~2% precision in form factor extraction.
- Controlled excited state contributions effectively.
- Identified the need to study multi-hadron contaminations.

## Abstract

We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_\mu(0)|\mathrm{B} ({\bf 0})\rangle$ 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.