${\overline{B}}^0$ and ${\overline{B}}_s^0$ decays into $J/\psi$ and $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2^{\prime }(1525)$, $K_2^{*}(1430)$

We make predictions for the ratios of branching fractions of ${\overline{B}}^0$ and ${\overline{B}}_s^0$ decays into $J/\psi$ and the scalar mesons $f_0(1370)$, $f_0(1710)$ or tensor mesons $f_2(1270)$, $f_2^{\prime }(1525)$, $K_2^{*}(1430)$. The theoretical approach is based on results of chiral unitary theory where these resonances are shown to be generated from the vector meson–vector meson interaction. Eight independent ratios can be predicted, and comparison is made with the recent data on ${\overline{B}}_s^0$ decay into $J/\psi f_2^{\prime }(1525)$ versus the ${\overline{B}}_s^0$ decay into $J/\psi f_2(1270)$.

Figure 1

Basic diagrams for ${\overline{B}}^0$ and ${\overline{B}}_s^0$ decay into $J/\psi$ and a $q\overline{q}$ pair [(a) and (c)], and hadronization of the $q\overline{q}$ components [(b) and (d)].

Figure 2

Decay mechanisms of $K^{*}{\overline{K}}^{*}+\pi \pi$, $K\overline{K}$ [(a) and (b)] and box diagrams considered in Ref. [20] to account for these decays [(c) and (d)].

Figure 3

Mechanisms to generated the vector-vector resonances through $VV$ rescattering. The dot of the vertex $RVV$ indicates the coupling of the resonance to the different $VV$ components. (a) for ${\overline{B}}^0$ decay, (b) for ${\overline{B}}_s^0$ decay.

Figure 4

Mechanisms for ${\overline{B}}^0\to J/\psi {\overline{K}}_2^{*}(1430)$ (a) and ${\overline{B}}_s^0\to J/\psi K_2^{*}(1430)$ (b).