Determination of $B$-meson distribution amplitudes from $B\to \pi ,K,D$ transition form factors

Abstract

Recent work on $B\to \pi$, $K$ and $B\to D$ form factors from lattice QCD and light-cone sum rules has made it possible to constrain the inverse moment ${\lambda }_B$ of the $B$-meson light-cone distribution amplitudes by performing a global fit of $B\to \pi ,K,D$ form factors. We have compiled the $B\to \pi ,K,D$ form factors calculated by the HPQCD, MILC, and RBC/UKQCD collaborations in the large $q^2$ region. By employing an three-parameter ansatz of the $B$-meson light-cone distribution amplitudes, we express the $B\to \pi ,K,D$ form factors at $q^2=0$ that are calculated from light-cone sum rules, in terms of the inverse moment ${\lambda }_B$ of the leading-twist $B$-meson light-cone distribution amplitude. In the $B\to \pi \ell \nu$ channel, we also include the available $q^2$-binned experimental data from the BaBar, Belle, and Belle~II collaborations. Using the Bourrely-Caprini-Lellouch parametrization, we perform a global fit and obtain ${\lambda }_B=217(19{)}_{-17}^{+82}$~MeV and $|V_{\text{ub}}|=3.68(13{)}_{-1}^{+0}\times 10^{-3}$. The second uncertainty is obtained by constraining ${\lambda }_B>200$ MeV and varying the inverse logarithmic moments ${\hat{\sigma }}_1\in [-0.7,0.7]$ and ${\hat{\sigma }}_2\in [-6,6]$, which represents the model-dependent uncertainty from the $B$-meson light-cone distribution amplitudes. When taking into account ${\lambda }_B$ and ${\hat{\sigma }}_1$ as fitting parameters simultaneously, the intervals of our preditions are ${\lambda }_B=[208,324]$~MeV and ${\hat{\sigma }}_1=[-0.7,0.27]$.

Comments: 18 pages, 7 figures