Isovector scalar a 0 ( 980 ) and a 0 ( 1450 ) resonances in the B → ψ ( K K ¯ , π η ) decays

We present an analysis of two isovector scalar resonant contributions to the $B$ decays into charmonia plus $K\overline{K}$ or $\ensuremath{\pi}\ensuremath{\eta}$ pair in the perturbative QCD approach. The Flatt\'e model for the ${a}_{0}(980)$ resonance and the Breit Wigner formula for the ${a}_{0}(1450)$ resonance are adopted to parametrize the timelike form factors in the dimeson distribution amplitudes, which capture the important final state interactions in these processes. The predicted distribution in the ${K}^{+}{K}^{\ensuremath{-}}$ invariant mass as well as its integrated branching ratio for the ${a}_{0}(980)$ resonance in the ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ mode agree well with the current available experimental data. The obtained branching ratio of the quasi-two-body decay ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{a}_{0}(980)(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\eta})$ can reach the order of ${10}^{\ensuremath{-}6}$, letting the corresponding measurement appear feasible. For the ${a}_{0}(1450)$ component, our results could be tested by further experiments in the LHCb and Belle II. We also discuss some theoretical uncertainties in detail in our calculation.