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 $Br(B_c\to {\eta }_{c}l\nu )=\left(9.31_{-2.01}^{+2.27}\right)\times 10^{-3}$.

12 pages, 16 figures

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• Uncertainties of the $B\to D$ transition form factor from the $D$-Meson Leading-Twist Distribution Amplitude
• $K_0^{\ast }(1430)$ Twist-2 Distribution Amplitude and $B_s,D_s\to K_0^{\ast }(1430)$ Transition Form Factors
• Investigating the ratio of CKM matrix elements $|V_{ub}|/|V_{cb}|$ from semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and kaon twist-2 distribution amplitude
• $a_0(980)$-meson twist-2 distribution amplitude within the QCD sum rules and investigation of $D\to a_0(980)(\to \eta \pi )e^{+}{\nu }_e$
• $a_1(1260)$-meson longitudinal twist-2 distribution amplitude and the $D\to a_1(1260){\ell }^{+}{\nu }_{\ell }$ decay processes
• Scrutinizing $B^0$-meson flavor changing neutral current decay into scalar $K_0^{\ast }(1430)$ meson with $b\to s{\ell }^{+}{\ell }^{-}(\nu \bar{\nu })$ transition
• ${\eta }_c$ leading-twist distribution amplitude and the $B_c\to {\eta }_c\ell {\bar{\nu }}_{\ell }$ semileptonic decays using QCD Sum Rules