Light-front approach to axial-vector quarkonium γ ^* γ ^* form factors

In this work, we perform a detailed study of transition form factors for axial- vector meson production via the two-photon fusion process γ^*γ^* → 1⁺⁺, with space-like virtual photons in the initial state and a P-wave axial-vector quarkonium in the final state. In this analysis, we employ the formalism of light-front quarkonium wave functions obtained from a solution of the Schrödinger equation for a selection of interquark potentials for QQ¯ interaction. We found the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any qq¯ axial-vector meson γ^*γ^* → 1⁺⁺ transition, while our numerical results are given for the phenomenologically relevant charmonium χ_c1 state. We present the helicity form factors as functions of both photon virtualities. We also obtain, that QF_LT(Q², 0)/F_TT(Q², 0) = const.