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

• Received 22 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.074025

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society