Light-Cone Distribution Amplitudes of Axial-vector Mesons

Abstract

We have presented a detailed study of twist-2 and twist-3 light-cone distribution amplitudes of $1^3{P}_1$ and $1^1{P}_1$ axial-vector mesons, based on QCD conformal partial wave expansion. Applying equations of motion, the twist-three two-parton light-cone distribution amplitudes can be expressed in terms of leading-twist and twist-three three-parton light-cone distribution amplitudes. The relevant G-parity invariant and violating parameters, containing the corrections due to the SU(3) breaking effects, are evaluated from the QCD sum rule method. The results for axial-vector decay constants of $1^3{P}_1$ states are presented. The values of tensor decay constants and Gegenbauer moments of the leading twist distribution amplitudes for $1^1{P}_1$ states are updated. Using Gell-Mann-Okubo mass formula, the mixing angle for the $f_8$ and $f_1$ of $1^3{P}_1$ states is ${\theta }_{{}^3{P}_1}\sim 38^{\circ }$, and that for $h_8$ and $h_1$ of $1^1{P}_1$ states is ${\theta }_{{}^1{P}_1}\sim 10^{\circ }$. The detailed properties for physical states $f_1(1285),f_1(1420),h_1(1170)$, and $h_1(1380)$ are given. Assuming the mixing angle between $K_{1A}$ and $K_{1B}$ to be ${\theta }_K=45^{\circ }$ or $-45^{\circ }$, we also give the detailed study for $K_1(1270)$ and $K_1(1400)$. Using the conformal partial wave expansion, we obtain the models for light-cone distribution amplitudes, containing contributions up to conformal spin 9/2. It is interesting to note that some distribution amplitudes have significant asymmetric behaviors, which should be phenomenologically attractive.

Comments: 77 pages. Typos corrected