Longitudinal leading-twist distribution amplitude of the J/ψ meson within the background field theory

We make a detailed study on the J/ψ meson longitudinal leading-twist distribution amplitude φ_2;J/ψ^∥ by using the QCD sum rules within the background field theory. By keeping all the nonperturbative condensates up to dimension 6, we obtain accurate QCD sum rules for the moments ⟨ξ_n;J/ψ^∥⟩. The first three ones are ⟨ξ_2;J/ψ^∥⟩=0.083(12), ⟨ξ_4;J/ψ^∥⟩=0.015(5), and ⟨ξ_6;J/ψ^∥⟩=0.003(2), respectively. Those values indicate a single peaked behavior for φ_2;J/ψ^∥. As an application, we adopt the QCD light-cone sum rules to calculate the Bc meson semileptonic decay Bc⁺→J/ψ⁺ν_. We obtain ${{Γ}}({B}c⁺{→}J/{ψ}{{}}⁺{{ν}}_{{}})=(89.6{7}_{{-}19.06}+24.76)×{}{10}^{{-}15} GeV$ and ${R}(J/{ψ}{{}}⁺{{ν}}_{{}})=0.21{7}_{{-}0.057}+0.069$, which agree with both the extrapolated next-to-leading order pQCD prediction and the new CDF measurement within errors.