Phenomenological model for $\gamma {\gamma }^{*}\to K{\overline{K}}^{*}\left(892\right)$ constraining the $f_1\left(1420\right)$ transition form factor

We present a phenomenological study of the $\gamma {\gamma }^{*}\to K{\overline{K}}^{*}\left(892\right)$ process by including the $s$-channel production of the $\eta \left(1475\right)$ and $f_1\left(1420\right)$ resonances. The nonresonant channel via $K$- and $K^{*}$-exchanges is investigated carefully by performing the Lorentz tensor decomposition and is constructed to yield a correct high-energy Regge behavior. The transition form factor of $f_1\left(1420\right)$ is adjusted to achieve a reasonable description of the existing L3 data in the $f_1\left(1420\right)$ resonance region. This model is intended to serve as a Monte Carlo generator for the analysis currently being performed by the BESIII Collaboration. We also estimate the polarized $\gamma {\gamma }^{*}\to K{\overline{K}}^{*}\left(892\right)$ cross sections and demonstrate how to extract the transition form factors of $f_1\left(1420\right)$ from the polarized cross sections.