Heavy Pseudoscalar Twist-3 Distribution Amplitudes within QCD Theory in Background Fields

Abstract

In this paper, we study the properties of the twist-3 distribution amplitude (DA) of the heavy pseudo-scalars such as ${\eta }_c$, $B_c$ and ${\eta }_b$. New sum rules for the twist-3 DA moments ${⟨{\xi }_P^n⟩}_{\mathrm{HP}}$ and ${⟨{\xi }_{\sigma }^n⟩}_{\mathrm{HP}}$ up to sixth orders and up to dimension-six condensates are deduced under the framework of the background field theory. Based on the sum rules for the twist-3 DA moments, we construct a new model for the two twist-3 DAs of the heavy pseudo-scalar with the help of the Brodsky-Huang-Lepage prescription. Furthermore, we apply them to the $B_c\to {\eta }_c$ transition form factor ($f_{+}^{B_c\to {\eta }_c}(q^2)$) within the light-cone sum rules approach, and the results are comparable with other approaches. It has been found that the twist-3 DAs ${\varphi }_{3;{\eta }_c}^P$ and ${\varphi }_{3;{\eta }_c}^{\sigma }$ are important for a reliable prediction of $f_{+}^{B_c\to {\eta }_c}(q^2)$. For example, at the maximum recoil region, we have $f_{+}^{B_c\to {\eta }_c}(0)=0.674\pm 0.066$, in which those two twist-3 terms provide $\sim 33\%$ and $\sim 22\%$ contributions. Also we calculate the branching ratio of the semi-leptonic decay $B_c\to {\eta }_{c}l\nu$ as $Br(B_c\to {\eta }_{c}l\nu )=\left(9.31_{-2.01}^{+2.27}\right)\times 10^{-3}$.

Comments: 12 pages, 16 figures