Light-front approach to axial-vector quarkonium $\gamma^* \gamma^*$ form factors

TL;DR

This paper investigates the transition form factors for axial-vector meson production via two-photon fusion using light-front quarkonium wave functions, providing a detailed theoretical framework and numerical results for charmonium states.

Contribution

It introduces a formalism for calculating axial-vector meson transition form factors with light-front wave functions and applies it to charmonium, including helicity structure and covariant decomposition.

Findings

Helicity form factors as functions of photon virtualities.

Constancy of the ratio Q F_LT(Q^2,0)/F_TT(Q^2,0).

Numerical results for the charmonium χ_c1 state.

Abstract

In this work, we perform a detailed study of transition form factors for axial-vector meson production via the two-photon fusion process $\gamma^* \gamma^* \to 1^{++}$, 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 Schr\"odinger 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 $\gamma^* \gamma^* \to 1^{++}$ 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 $Q F_{\rm LT}(Q^2,0)/F_{\rm TT}(Q^2,0) = {\rm const.}$