The longitudinal leading-twist distribution amplitude of $J/\ddot{I}ˆ$ meson within background field theory

Abstract

We make a detailed study on the $J/\ddot{I}ˆ$ meson longitudinal leading-twist distribution amplitude $\ddot{I}{•}_{2;J/\ddot{I}ˆ}^{\Vert }$ by using the QCD sum rules within the background field theory. By keeping all the non-perturbative condensates up to dimension-six, we obtain accurate QCD sum rules for the moments $⟨\hat{I}{¾}_{n;J/\ddot{I}ˆ}^{\Vert }⟩$. The first three ones are $⟨\hat{I}{¾}_{2;J/\ddot{I}ˆ}^{\Vert }⟩=0.083(12)$, $⟨\hat{I}{¾}_{4;J/\ddot{I}ˆ}^{\Vert }⟩=0.015(5)$ and $⟨\hat{I}{¾}_{6;J/\ddot{I}ˆ}^{\Vert }⟩=0.003(2)$, leading to a single peaked behavior for $\ddot{I}{•}_{2;J/\ddot{I}ˆ}^{\Vert }$ which is sharper than the previous ones around the region of $x\sim 0.5$. As an application, we adopt the QCD light-cone sum rules to calculate the $B_c$ meson semileptonic decay $B_c^{+}\to J/\ddot{I}ˆ{\ell }^{+}\hat{I}{½}_{\ell }$. We obtain $\hat{I}“(B_c^{+}\to J/\ddot{I}ˆ{\ell }^{+}\hat{I}{½}_{\ell })=(89.67_{-19.06}^{+24.76})\times 10^{-15}\mathrm{GeV}$ and $\Re (J/\ddot{I}ˆ{\ell }^{+}\hat{I}{½}_{\ell })=0.217_{-0.057}^{+0.069}$, which agree with the next-to-leading order pQCD prediction and the new CDF measurement within errors.

10 pages, 4 figures