B 0 and B 0 s decays into J /ψ f 0 (980) and J /ψ f 0 (500) and the nature of the scalar resonances We describe the B 0 and B 0 s decays into J /ψ f 0 (500) and J /ψ f 0 (980) by taking into account the dominant process for the weak decay of B 0 and B 0 s 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 mesonmeson components, described in terms of chiral unitary theory, gives rise to the f 0 (980) and f 0 (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 /ψ f 0 (980) and J /ψ f 0 (500) for each of the B decays in quantitative agreement with experiment, with the f 0 (980) clearly dominant in the B 0 s decay and the f 0 (500) in the B 0 decay.