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

Abstract

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 $a_n(μ)$, $ξ$-moment $\langle ξ^n\rangle^{\parallel(\perp)}$ 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 $\langle ξ^n\rangle^\perp>\langle ξ^n\rangle^\parallel$. 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 $φ_{2}^\parallel(x)\simeqφ_{3}^\perp(x)$. 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., $φ_{2}^A(x)\simeqφ_{2}^\parallel(x)$ and $φ_{3}^P(x)\simeqφ_{3}^\perp(x)$ in $m_q\rightarrow\infty$. This reveals the spin independence of LCDAs in the heavy quark limit. Furthermore, it is found $φ^A_2(x)\simeqφ_2^\parallel(x)\approxφ_3^P(x)\simeqφ_3^\perp(x)$ with the replacement $M\rightarrow M_0$ and in the heavy quark limit.

Figures (5)

• Figure 1: The twist-2 $\phi_2^\parallel(x)$ (the red line) and twist-3 $\phi_3^\perp(x)$ (the blue line) LCDAs of $\rho$ and $K^*$.
• Figure 2: The twist-2 $\phi_2(x)$ ($\phi_2^A(x)$, $\phi_2^\parallel(x)$) and twist-3 $\phi_3(x)$ ($\phi_3^P(x)$, $\phi_3^\perp(x)$) LCDAs of $\pi$/$\rho$ and $K$/$K^*$ mesons, in which the dashed and solid lines are the LCDAs of pseudoscalar and vector mesons, respectively.
• Figure 3: Same as in FIG. \ref{['1']} but with the $D^*_{(s)}$ and $B^*_{(s/c)}$ mesons.
• Figure 4: Same as in FIG. \ref{['2']} but with the $D_{(s)}$/$D^*_{(s)}$ and $B_{(s/c)}$/$B^*_{(s/c)}$ mesons.
• Figure 5: Full results (red) and $\mathbf{k}_\perp^2$-term contributions (light-colored) for the twist-2 LCDAs of the $K^*$ and $B_c^*$ mesons.