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arXiv · 2208.05377

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

Izabela Babiarz·Roman Pasechnik·Wolfgang Schäfer·Antoni Szczurek
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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 $Q F_{\rm LT}(Q^2,0)/F_{\rm TT}(Q^2,0) = {\rm const.}$

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Izabela Babiarz, Roman Pasechnik, Wolfgang Schäfer, Antoni Szczurek. 2022-08-10. Light-front approach to axial-vector quarkonium $\gamma^* \gamma^*$ form factors. https://doi.org/10.1007/jhep09(2022)170

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