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 self-consistent light-front quark model, and the $n$th Gegenbauer moment $a_n(\hat{I}¼)$, $\hat{I}¾$-moment $⟨\hat{I}{¾}^n{⟩}^{\parallel (\perp )}$ and transverse moment $⟨{\mathbf{k}}_{\perp }^n{⟩}^{\parallel (\perp )}$ 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 $⟨\hat{I}{¾}^n{⟩}^{\perp }>⟨\hat{I}{¾}^n{⟩}^{\parallel }$. This is consistent 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 $\ddot{I}{•}_2^{\parallel }(x)\simeq \ddot{I}{•}_3^{\perp }(x)$. 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., $\ddot{I}{•}_2^A(x)\simeq \ddot{I}{•}_2^{\parallel }(x)$ and $\ddot{I}{•}_3^P(x)\simeq \ddot{I}{•}_3^{\perp }(x)$ in $m_q\to \infty$. In the heavy-quark limit within the self-consistent LFQM framework, we find an approximate correlated spin-twist independence pattern, with $\ddot{I}{•}_2^A(x)\simeq \ddot{I}{•}_2^{\parallel }(x)\approx \ddot{I}{•}_3^P(x)\simeq \ddot{I}{•}_3^{\perp }(x)$, resulting from the suppression of twist dependence and the approximate spin independence between pseudoscalar and vector mesons.

10 pages, 5 figures, Version accepted for publication in PLB