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 $|V_{\text{ub}}|=3.68(13)_{-1}^{+0}\times10^{-3}$. 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 $\hat{\sigma}_1=[-0.7, 0.27]$.