Lattice QCD calculation of $\bar{B}\to Dl\bar{\nu}$ decay form factors at zero recoil

TL;DR

This paper presents a high-precision lattice QCD calculation of the $ar{B} o Dlar{ u}$ decay form factors at zero recoil, crucial for understanding B-meson decays and testing the Standard Model.

Contribution

The study introduces a ratio method to accurately compute decay form factors and directly assesses heavy quark mass dependence with multiple mass combinations.

Findings

Precise values for $h_+(1)$ and $h_-(1)$ form factors.

Determination of the physical $F_{B o D}(1)$ with quantified uncertainties.

Analysis of heavy quark mass effects and systematic errors.

Abstract

A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors is presented. We obtain the value of the form factor $h_+(w)$ at the zero-recoil limit $w=1$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar ratio. In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses. Our results are $h_+(1) = 1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{10}_{30})$. For both the first error is statistical, the second stems from the uncertainty in adjusting the heavy quark masses, and the last from omitted radiative corrections. Combining these results, we obtain a precise determination of the physical combination $F_{B\to D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in quadrature. The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of $F_{B\to D}-1$.