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

We study the decay processes of ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}{K}^0$ and ${\overline{B}}^0\to J/\psi f_1(1285)$ to analyze the $f_1(1285)$ resonance. By the calculation within chiral unitary approach where $f_1(1285)$ resonance is dynamically generated from the $K^{*}\overline{K}-\mathrm{c}.\mathrm{c}.$ interaction, we find that the ${\overline{K}}^{*0}{K}^0$ 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 $R_t={\mathrm{\Gamma }}_{{\overline{B}}^0\to J/\psi {\overline{K}}^{*0}{K}^0}/{\mathrm{\Gamma }}_{{\overline{B}}^0\to J/\psi f_1(1285)}$ which is expected to be compared with the experimental data.

Figure 1

The ${\overline{B}}^0\to J/\psi f_1(1285)$ decay process at the quark level. (a) Elementary quark arrangement for the weak decay of $b$ quark. (b) Hadronization of the $d\overline{d}$ component.

Figure 2

Diagrammatic representation for the ${\overline{B}}^0\to J/\psi VP$ process. (a) The reaction at the tree level. (b) The rescattering between pseudoscalar mesons and vector mesons. (c) Production process of the ${\overline{B}}^0\to J/\psi f_1(1285)$ decay.

Figure 3

The total contributions for the ${\overline{K}}^{*0}{K}^0$ production. Subfigures (a) and (d) have a minus sign corresponding with subfigures (b) and (c).

Figure 4

Dalitz plot for ${\overline{K}}^{*0}{K}^0$ and $J/\psi {\overline{K}}^{*0}$ invariant masses in the ${\overline{B}}^0\to J/\psi {\overline{K}}^{*0}{K}^0$ decay.

Figure 5

The distribution of $R_{\mathrm{\Gamma }}$ as a function of the invariant mass $M_{\mathrm{inv}}$ of ${\overline{K}}^{*0}{K}^0$ at $\mu =1100\mathrm{MeV},1200\mathrm{MeV}$ and 1300 MeV, respectively. The solid (dashed) curve represents the dynamically generated prediction with (without) the polarization structure factor. The dot-dashed curve stands for the phase space distribution which has been normalized to make it have the same area with the solid curve in the $M_{\mathrm{inv}}$ range.