Light-cone Distribution Amplitudes of Vector Mesons within the Self-Consistent Light-front Quark Model

In this paper, we investigate the twist-2 and twist-3 light-cone distribution amplitudes (LCDAs) of vector mesons within the light-front quark model, and the $n$th Gegenbauer moment $a_n(\mu)$, $\xi$-moment $\langle \xi^n\rangle^{\parallel(\perp)}$ and transverse moment $\langle \mathbf{k}^n_\perp\rangle^{\parallel(\perp)}$ are also carried out. Adopting the parameter set fixed by confinements from the mesonic decay constants, we perform the numerical analysis and the results reveal several key insights: (i) The flavor symmetry breaking effects are more pronounced in the twist-3 LCDAs of vector mesons, which leads to the establishment of $a_1^\perp>a_1^\parallel$ and $\langle \xi^n\rangle^\perp>\langle \xi^n\rangle^\parallel$. This consists with previous findings in research for the LCDAs of pseudoscalar mesons. (ii) For vector mesons, the twist dependence decreases in the heavy quark limit which lead to $\phi_{2}^\parallel(x)\simeq\phi_{3}^\perp(x)$. For pseudoscalar and vector mesons composed of the same quark constituents, their LCDAs with the same twist exhibit similarity and gradually converge as the increasing of quark mass, i.e., $\phi_{2}^A(x)\simeq\phi_{2}^\parallel(x)$ and $\phi_{3}^P(x)\simeq\phi_{3}^\perp(x)$ in $m_q\rightarrow\infty$. This reveals the spin independence of LCDAs in the heavy quark limit. Furthermore, it is found $\phi^A_2(x)\simeq\phi_2^\parallel(x)\approx\phi_3^P(x)\simeq\phi_3^\perp(x)$ with the replacement $M\rightarrow M_0$ and in the heavy quark limit.