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

A bstract 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 q 2 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 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 → πℓν 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 = $$ 217{(19)}_{-17}^{+82} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>217</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mn>19</mml:mn> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>82</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> MeV and | V ub | = $$ 3.68{(13)}_{-1}^{+0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3.68</mml:mn> <mml:msubsup> <mml:mfenced> <mml:mn>13</mml:mn> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> × 10 −3 . The second uncertainty is obtained by constraining λ B &gt; 200 MeV and varying the inverse logarithmic moments $$ {\hat{\sigma}}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>σ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> ∈ [−0.7, 0.7] and $$ {\hat{\sigma}}_2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>σ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ∈ [−6, 6], which represents the model-dependent uncertainty from the B -meson light-cone distribution amplitudes. When taking into account λ B and $$ {\hat{\sigma}}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>σ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> as fitting parameters simultaneously, the intervals of our preditions are λ B = [208, 324] MeV and $$ {\hat{\sigma}}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>σ</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> = [−0.7, 0.27].