Recent work on B → π, K and B → D form factors from lattice QCD and light-cone sum rules has made it possible to constrain the inverse moment λB of the B-meson light-cone distribution amplitudes by performing a global fit of B → π, K, D form factors. We have compiled the B → π, K, D form factors calculated by the HPQCD, MILC, and RBC/UKQCD collaborations in the large q2 region. By employing an three-parameter ansatz of the B-meson light-cone distribution amplitudes, we express the B → π, K, D form factors at q2 = 0 that are calculated from light-cone sum rules, in terms of the inverse moment λB of the leading-twist B-meson light-cone distribution amplitude. In the B → πℓν channel, we also include the available q2-binned experimental data from the BaBar, Belle, and Belle II collaborations. Using the Bourrely-Caprini-Lellouch parametrization, we perform a global fit and obtain λB = <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mn>217</mn> <msubsup> <mfenced close=")" open="("> <mn>19</mn> </mfenced> <mrow> <mo>−</mo> <mn>17</mn> </mrow> <mrow> <mo>+</mo> <mn>82</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ 217{(19)}_{-17}^{+82} $</EquationSource> </InlineEquation> MeV and |Vub| = <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mn>3.68</mn> <msubsup> <mfenced close=")" open="("> <mn>13</mn> </mfenced> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mo>+</mo> <mn>0</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ 3.68{(13)}_{-1}^{+0} $</EquationSource> </InlineEquation> × 10−3. The second uncertainty is obtained by constraining λB > 200 MeV and varying the inverse logarithmic moments <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">̂</mo> </mover> <mn>1</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\hat{\sigma}}_1 $</EquationSource> </InlineEquation> ∈ [−0.7, 0.7] and <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">̂</mo> </mover> <mn>2</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\hat{\sigma}}_2 $</EquationSource> </InlineEquation> ∈ [−6, 6], which represents the model-dependent uncertainty from the B-meson light-cone distribution amplitudes. When taking into account λB and <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">̂</mo> </mover> <mn>1</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\hat{\sigma}}_1 $</EquationSource> </InlineEquation> as fitting parameters simultaneously, the intervals of our preditions are λB = [208, 324] MeV and <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">̂</mo> </mover> <mn>1</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\hat{\sigma}}_1 $</EquationSource> </InlineEquation> = [−0.7, 0.27].

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

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2026年5月12日

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Dong-Hao Li,
Cai-Dian Lü,
Ulf-G. Meißner,
Jing Gao

摘要

Recent work on B → π, K and B → 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 → π, K, D form factors. We have compiled the B → π, K, D form factors calculated by the HPQCD, MILC, and RBC/UKQCD collaborations in the large q² region. By employing an three-parameter ansatz of the B-meson light-cone distribution amplitudes, we express the B → π, K, D form factors at q² = 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 → πℓν channel, we also include the available q²-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 = $217 {(19)}_{- 17}^{+ 82}$ $ 217{(19)}_{-17}^{+82} $ MeV and |V_ub| = $3.68 {(13)}_{- 1}^{+ 0}$ $ 3.68{(13)}_{-1}^{+0} $ × 10⁻³. The second uncertainty is obtained by constraining λ_B > 200 MeV and varying the inverse logarithmic moments ${\hat{σ}}_{1}$ $ {\hat{\sigma}}_1 $ ∈ [−0.7, 0.7] and ${\hat{σ}}_{2}$ $ {\hat{\sigma}}_2 $ ∈ [−6, 6], which represents the model-dependent uncertainty from the B-meson light-cone distribution amplitudes. When taking into account λ_B and ${\hat{σ}}_{1}$ $ {\hat{\sigma}}_1 $ as fitting parameters simultaneously, the intervals of our preditions are λ_B = [208, 324] MeV and ${\hat{σ}}_{1}$ $ {\hat{\sigma}}_1 $ = [−0.7, 0.27].