Constraints on the Leading-Twist Pion Distribution Amplitude from A QCD Light-Cone Sum Rule with Chiral Current

Abstract

We present an improved analysis of the constraints on the first two Gegenbauer moments, $a_2^{\pi }$ and $a_4^{\pi }$, of the pion's leading-twist distribution amplitude from a QCD light-cone sum rule analysis of $B\to \pi$ weak transition form factor $f_{+}(q^2)$. Proper chiral current is adopted in QCD light-cone sum rule so as to eliminate the most uncertain twist-3 contributions to $f_{+}(q^2)$, and then we concentrate our attention on the properties of the leading-twist pion DA. A nearly model-independent $f_{+}(q^2)$ as shown in Ref.\cite{pball0} that is based on the spectrum of $B\to \pi l\nu$ decays from BaBar, together with their uncertainties, are adopted as the standard shape for $f_{+}(q^2)$ to do our discussion. From a minimum ${\chi }^2$-fit and by taking the theoretical uncertainties into account, we obtain $a_2^{\pi }(1GeV)=0.17_{-0.17}^{+0.15}$ and $a_4^{\pi }(1GeV)=-0.06_{-0.22}^{+0.20}$ at the $1\sigma$ confidence level for $m_b^{\ast }\in [4.7,4,8]GeV$.

Comments: 10 pages, 4 figures. References added. To be published in EPJC