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

Abstract

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 $(h=\pm 1)$ polarizations, two types of decay constants, $f_ρ^{\parallel}$ and $f_ρ^{\perp}$, arises accordingly. We demonstrate that these decay constants can be self-consistently extracted from both local ($z^μ=0$) and nonlocal ($z^μ\neq 0$) matrix elements $\langle 0 | \bar{q}(z)\, Γ\, q(-z) | ρ(P,h) \rangle$, with $Γ= (γ^μ, σ^{μν}, γ^μγ_5, \mathbf{1})$, 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 $f_ρ^{\parallel}$ and $f_ρ^{\perp}$ 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 ($ϕ_{2;\mathrm{V}}^\parallel, ϕ_{3;\mathrm{V}}^\parallel, ψ_{3;\mathrm{A}}^\perp, ϕ_{4;\mathrm{V}}^\parallel$) and chiral-odd DAs ($ϕ_{2;\mathrm{T}}^\perp, ϕ_{3;\mathrm{T}}^\perp, ψ_{3;\mathrm{S}}^\parallel, ϕ_{4;\mathrm{T}}^\perp$) 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.