Beyond leading twist: $ρ$ meson decay constants and distribution amplitudes in a self-consistent light-front quark model

In this study, we present a comprehensive analysis of decay constants and chiral-even and chiral-odd distribution amplitudes (DAs) up to twist 4 for the $ρ$ meson in the standard light-front quark model (LFQM) based on the Bakamjian-Thomas (BT) construction. For the $ρ$ meson, which possesses both longitudinal $(h=0)$ and transverse (h=± 1) polarizations, two types of decay constants, f_ρ∥ and f_ρ⊥, arises accordingly. We demonstrate that these decay constants can be self-consistently extracted from both local (z^μ=0) and nonlocal (z^μ≠ 0) matrix elements 0 | q̄(z)\, Γ\, q(-z) | ρ(P,h), with Γ= (γ^μ, σμν, γ^μγ₅, 1), in a manner independent of current components, polarizations, and reference frames. In particular, we emphasize the role of nonlocal matrix elements involving axial-vector and scalar currents, where mixing between f_ρ∥ and f_ρ⊥ occurs. We show that this mixing is consistently resolved through the BT construction, ensuring the proper extraction of these decay constants. Additionally, we investigate the structure of chiral-even DAs (ϕ2;V^∥, ϕ3;V^∥, ψ3;A^⊥, ϕ4;V^∥) and chiral-odd DAs (ϕ2;T^⊥, ϕ3;T^⊥, ψ3;S^∥, ϕ4;T^⊥) beyond leading twists, and present their corresponding $ξ$-moments and Gegenbauer moments. These results provide deeper insight into the nonperturbative structure of vector mesons and demonstrate the robustness and self-consistency of the LFQM based on the BT framework.