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.

10 pages, 4 figures

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• Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory
• QCD corrections to the $B_c$ to charmonia semi-leptonic decays
• The $\rho$-meson longitudinal leading-twist distribution amplitude within QCD background field theory
• The $\rho$-meson longitudinal leading-twist distribution amplitude
• Reconsideration of the $B\to K^{\ast }$ Transition Form Factors within the QCD Light-Cone Sum Rules
• Measurement of the $B_c^{\pm }$ production cross section in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

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• Scrutinizing New Physics in Semi-leptonic $B_c\to J/\psi \tau \nu$ Decay
• Relativistic calculations of $R(D^{(\ast )})$, $R(D_s^{(\ast )})$, $R({\eta }_c)$ and $R(J/\psi )$
• The light front wave functions and diffractive electroproduction of vector mesons
• $B_c\to J/\psi$ helicity form factors and the $B_c^{+}\to J/\psi +(P,V,{\ell }^{+}{\nu }_{\ell })$ decays
• Revisiting the production of $J/\psi +{\eta }_c$ via the $e^{+}{e}^{-}$ annihilation within the QCD light-cone sum rules
• Probing $D_s^{\ast }$-meson longitudinal twist-2 LCDA
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• ${\eta }_c$ leading-twist distribution amplitude and the $B_c\to {\eta }_c\ell {\bar{\nu }}_{\ell }$ semileptonic decays using QCD Sum Rules