The $\ddot{I}$-meson longitudinal leading-twist distribution amplitude

Abstract

In the present paper, we suggest a convenient model for the vector $\ddot{I}$-meson longitudinal leading-twist distribution amplitude $\ddot{I}{•}_{2;\ddot{I}}^{\Vert }$, whose distribution is controlled by a single parameter $B_{2;\ddot{I}}^{\Vert }$. By choosing proper chiral current in the correlator, we obtain new light-cone sum rules (LCSR) for the $B\to \ddot{I}$ TFFs $A_1$, $A_2$ and $V$, in which the $\hat{I}{´}^1$-order $\ddot{I}{•}_{2;\ddot{I}}^{\Vert }$ provides dominant contributions. Then we make a detailed discussion on the $\ddot{I}{•}_{2;\ddot{I}}^{\Vert }$ properties via those $B\to \ddot{I}$ TFFs. A proper choice of $B_{2;\ddot{I}}^{\Vert }$ can make all the TFFs agree with the lattice QCD predictions. A prediction of $|V_{\mathrm{ub}}|$ has also been presented by using the extrapolated TFFs, which indicates that a larger $B_{2;\ddot{I}}^{\Vert }$ leads to a larger $|V_{\mathrm{ub}}|$. To compare with the BABAR data on $|V_{\mathrm{ub}}|$, the longitudinal leading-twist DA $\ddot{I}{•}_{2;\ddot{I}}^{\Vert }$ prefers a doubly-humped behavior.

7 pages, 3 figures. Discussions improved and references updated. To be published in Phys.Lett.B