Theoretical study in the $\bar{B}^0 \to J/\psi \bar{K}^{*0} K^0$ and $\bar{B}^0 \to J/\psi f_1(1285)$ decays

We study the decay processes of $\bar{B}^0 \to J/\psi \bar{K}^{*0} K^0$ and $\bar{B}^0 \to J/\psi f_1(1285)$ to analyse the $f_1(1285)$ resonance. By the calculation within chiral unitary approach where $f_1(1285)$ resonance is dynamically generated from the $K^*\bar{K}-c.c.$ interaction, we find that the $\bar{K}^{*0} K^0$ invariant mass distribution has a clear broad peak. Such broad peak has been understood as the signal of the $f_1(1285)$. Finally, we obtain a theoretical result $R_t=\Gamma_{\bar{B}^0 \to J/\psi \bar{K}^{*0} K^0}/\Gamma_{\bar{B}^0 \to J/\psi f_1(1285)}$ which is expected to be compared with the experimental data.