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

Abstract

In this paper, we study the leading-twist distribution amplitude (DA) of the heavy pseudoscalars (HPs), such as ${\eta }_c$, ${\eta }_b$ and $B_c$, within the QCD theory in the background fields. New sum rules up to dimension-six condensates for both the HP decay constants and their leading-twist DA moments are presented. From the sum rules for the HP decay constants, we obtain $f_{{\eta }_c}=453\pm 4\text{MeV}$, $f_{B_c}=498\pm 14\text{MeV}$, and $f_{{\eta }_b}=811\pm 34\text{MeV}$. Basing on the sum rules for the HPs' leading-twist DA moments, we construct a new model for the ${\eta }_c$, ${\eta }_b$ and $B_c$ leading-twist DAs. Our present HP DA model can also be adaptable for the light pseudo-scalar DAs, such as the pion and kaon DAs. Thus, it shall be applicable for a wide range of QCD exclusive processes. As an application, we apply the ${\eta }_c$ leading-twist DA to calculate the $B_c\to {\eta }_c$ transition form factor $f_{+}^{B_c\to {\eta }_c}(q^2)$. At the maximum recoil region, we obtain $f_{+}^{B_c\to {\eta }_c}(0)=0.612_{-0.052}^{+0.053}$. After further extrapolating the TFF $f_{+}^{B_c\to {\eta }_c}(q^2)$ to its allowable $q^2$ region, we predict the branching ratio for the semi-leptonic decay $B_c\to {\eta }_{c}l\nu$. We obtain $\mathcal{B}(B_c\to {\eta }_{c}l\nu )=\left(7.70_{-1.48}^{+1.65}\right)\times 10^{-3}$ for massless leptons, which is consistent with the LCSRs estimation obtained in the literature.

Comments: 14 pages, 14 figures