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

TL;DR

This paper refines constraints on the pion's leading-twist distribution amplitude by analyzing $B o\pi$ form factors using QCD light-cone sum rules with chiral currents, reducing uncertainties from twist-3 contributions.

Contribution

It introduces an improved method to determine the first two Gegenbauer moments of the pion distribution amplitude by eliminating twist-3 uncertainties and using a nearly model-independent form factor shape.

Findings

Estimated $a_2^\pi(1GeV)$ as 0.17 with uncertainties

Estimated $a_4^\pi(1GeV)$ as -0.06 with uncertainties

Reduced theoretical uncertainties in pion DA parameters

Abstract

We present an improved analysis of the constraints on the first two Gegenbauer moments, $a^\pi_2$ and $a^\pi_4$, 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 $a^\pi_2(1GeV)=0.17^{+0.15}_{-0.17}$ and $a^\pi_4(1GeV)=-0.06^{+0.20}_{-0.22}$ at the $1\sigma$ confidence level for $m^*_b\in[4.7,4,8] GeV$.