Light-front approach to axial-vector quarkonium ${\gamma }^{\ast }{\gamma }^{\ast }$ form factors

Abstract

In this work, we perform a detailed study of transition form factors for axial-vector meson production via the two-photon fusion process ${\gamma }^{\ast }{\gamma }^{\ast }\to 1^{++}$, 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 $Q\bar{Q}$ interaction. We found the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any $q\bar{q}$ axial-vector meson ${\gamma }^{\ast }{\gamma }^{\ast }\to 1^{++}$ transition, while our numerical results are given for the phenomenologically relevant charmonium ${\chi }_{c1}$ state. We present the helicity form factors as functions of both photon virtualities. We also obtain, that $Q{F}_{\mathrm{LT}}(Q^2,0)/F_{\mathrm{TT}}(Q^2,0)=const.$

Comments: 25 pages, 7 figures