Phenomenological model for $\gamma {\gamma }^{\ast }\to K{\bar{K}}^{\ast }(892)$ constraining the $f_1(1420)$ transition form factor

We present a phenomenological study of the $\gamma {\gamma }^{\ast }\to K{\bar{K}}^{\ast }(892)$ process by including the $s$-channel production of the $\eta (1475)$ and $f_1(1420)$ resonances. The non-resonant channel via $K$- and $K^{\ast }$-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 $f_1(1420)$ is adjusted to achieve a reasonable description of the existing L3 data in the $f_1(1420)$ 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 $\gamma {\gamma }^{\ast }\to K{\bar{K}}^{\ast }(892)$ cross sections and demonstrate how to extract the transition form factors of $f_1(1420)$ from the polarized cross sections.