The longitudinal leading-twist distribution amplitude of $J/\psi$ meson within background field theory

Abstract

We make a detailed study on the $J/\psi$ meson longitudinal leading-twist distribution amplitude ${\varphi }_{2;J/\psi }^{\Vert }$ 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 $⟨{\xi }_{n;J/\psi }^{\Vert }⟩$. The first three ones are $⟨{\xi }_{2;J/\psi }^{\Vert }⟩=0.083(12)$, $⟨{\xi }_{4;J/\psi }^{\Vert }⟩=0.015(5)$ and $⟨{\xi }_{6;J/\psi }^{\Vert }⟩=0.003(2)$, leading to a single peaked behavior for ${\varphi }_{2;J/\psi }^{\Vert }$ 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 $B_c^{+}\to J/\psi {\ell }^{+}{\nu }_{\ell }$. We obtain $\Gamma (B_c^{+}\to J/\psi {\ell }^{+}{\nu }_{\ell })=(89.67_{-19.06}^{+24.76})\times 10^{-15}\mathrm{GeV}$ and $\Re (J/\psi {\ell }^{+}{\nu }_{\ell })=0.217_{-0.057}^{+0.069}$, which agree with the next-to-leading order pQCD prediction and the new CDF measurement within errors.

Comments: 10 pages, 4 figures