Study the $$B^{0}_{(s)}$$ decays into $$\phi $$ and a scalar or vector meson

In the present work, we investigate the decays of $$B^{0}_{(s)} \rightarrow \phi \pi ^{+}\pi ^{-}$$ B ( s ) 0 → ϕ π + π - with the final state interaction based on the chiral unitary approach. In the final state interaction of the $$\pi ^+\pi ^-$$ π + π - with its coupled channels, we study the effects of the $$\eta \eta $$ η η channel in the two-body interaction for the reproduction of the $$f_{0}(980)$$ f 0 ( 980 ) state, where its contribution to the $$f_{0}(980)$$ f 0 ( 980 ) state can be ignored. Our results for the $$\pi ^+\pi ^-$$ π + π - invariant mass distributions of the decay $$B^{0}_{s} \rightarrow \phi \pi ^{+}\pi ^{-}$$ B s 0 → ϕ π + π - describe the experimental data up to 1 GeV well, with the resonance contributions from the $$f_{0}(980)$$ f 0 ( 980 ) and $$\rho $$ ρ . For the predicted invariant mass distributions of the $$B^{0} \rightarrow \phi \pi ^{+}\pi ^{-}$$ B 0 → ϕ π + π - decay, we find that the contributions from the $$f_{0}(500)$$ f 0 ( 500 ) are significant, but not from the $$f_{0}(980)$$ f 0 ( 980 ) state. With some experimental branching ratios to determine the production vertex factors, we make predictions for the branching ratios of the other decay channels, including the vector mesons, in the $$B^0_{(s)}$$ B ( s ) 0 decays, some of which are consistent with the experimental measurements within the uncertainties.