Determination of $B$-meson distribution amplitudes from $B o π,K,D$ transition form factors

Recent work on $B \to π$, $K$ and $B\to D$ form factors from lattice QCD and light-cone sum rules has made it possible to constrain the inverse moment $λ_B$ of the $B$-meson light-cone distribution amplitudes by performing a global fit of $B\to π,K,D$ form factors. We have compiled the $B\to π,K,D$ 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 $B\to π,K,D$ form factors at $q^2=0$ that are calculated from light-cone sum rules, in terms of the inverse moment $λ_B$ of the leading-twist $B$-meson light-cone distribution amplitude. In the $B \to π\ell ν$ 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 $λ_B=217(19){-17}^{+82}$~MeV and $|V{\text{ub}}|=3.68(13)_{-1}^{+0}\times10^{-3}$. The second uncertainty is obtained by constraining $λ_B>200$ MeV and varying the inverse logarithmic moments $\hatσ_1\in[-0.7,0.7]$ and $\hatσ_2\in[-6,6]$, which represents the model-dependent uncertainty from the $B$-meson light-cone distribution amplitudes. When taking into account $λ_B$ and $\hatσ_1$ as fitting parameters simultaneously, the intervals of our preditions are $λ_B=[208, 324]$~MeV and $\hatσ_1=[-0.7, 0.27]$.

💡 Research Summary

This paper presents a comprehensive global analysis aimed at determining a fundamental non-perturbative parameter of the B-meson, the inverse moment λ_B of its leading-twist light-cone distribution amplitude (LCDA). The LCDA describes the momentum distribution of the light spectator quark inside the B-meson and is a critical input for theoretical predictions of exclusive B-decays, particularly in the framework of QCD factorization and light-cone sum rules (LCSR). Precise knowledge of λ_B is essential for reducing theoretical uncertainties in extracting CKM matrix elements like |V_ub| from semi-leptonic decays.

The authors’ strategy involves a simultaneous fit to transition form factor data for three distinct channels: B → π, B → K, and B → D. They combine three complementary sources of information:

1. High-precision Lattice QCD data in the large q^2 (low recoil) region from the HPQCD, MILC, and RBC/UKQCD collaborations.
2. Theoretical LCSR predictions in the large recoil (small q^2) region, where the form factors are expressed as functions of λ_B within a specific three-parameter model for the B-meson LCDA.
3. Experimental data on q^2-binned differential branching fractions for B → π ℓ ν from the BaBar, Belle, and Belle II experiments.

To connect the low and high q^2 regions, the q^2-dependence of the form factors is parameterized using the Bourrely-Caprini-Lellouch (BCL) expansion. A global χ^2 fit is then performed, treating the BCL parameters, |V_ub|, and λ_B as free parameters to be constrained by the combined dataset.

The main results of this global analysis are:

• λ_B = 217(19)^{+82}_{-17} MeV.
• |V_ub| = 3.68(13)^{+0}_{-1} × 10^{-3}. The first uncertainty is statistical from the fit, while the second, asymmetric uncertainty is systematic, originating from the model-dependence of the B-meson LCDA. This is evaluated by varying the inverse logarithmic moments σ̂₁ and σ̂₂ within conservative ranges. In an alternative fit where both λ_B and σ̂₁ are treated as free parameters, the authors find allowed intervals of λ_B =