B⁰ and B_s⁰ decays into J/ψf₀(980) and J/ψf₀(500) and the nature of the scalar resonances

We describe the B⁰ and B_s⁰ decays into J/ψf₀(500) and J/ψf₀(980) by taking into account the dominant process for the weak decay of B⁰ and B_s⁰ into J/ψ and a qq^¯ component. After hadronization of this qq^¯ component into pairs of pseudoscalar mesons we obtain certain weights for the meson–meson components and allow them to interact among themselves. The final state interaction of the meson–meson components, described in terms of chiral unitary theory, gives rise to the f₀(980) and f₀(500) resonances and we can obtain the π⁺π⁻ invariant mass distributions after the decay of the resonances, which allows us to compare directly to the experiments. We obtain ratios of J/ψf₀(980) and J/ψf₀(500) for each of the B decays in quantitative agreement with experiment, with the f₀(980) clearly dominant in the B_s⁰ decay and the f₀(500) in the B⁰ decay