<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mi>η</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> transition form factors for spacelike photons

We derive the light-front wave function (LFWF) representation of the ${\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}(1S),{\ensuremath{\eta}}_{c}(2S)$ transition form factor $F({Q}_{1}^{2},{Q}_{2}^{2})$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schr\"odinger equation for a variety of $c\overline{c}$ potentials. We compare our results to the BABAR experimental data for the ${\ensuremath{\eta}}_{c}(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behavior is strongly delayed and discuss applicability of the collinear and/or massless limit. We present some examples of two-dimensional distributions for $F({Q}_{1}^{2},{Q}_{2}^{2})$. A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be almost model independent. Factorization is shown to be strongly broken, and a scaling of the form factor as a function of ${\overline{Q}}^{2}=({Q}_{1}^{2}+{Q}_{2}^{2})/2$ is obtained.

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