Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson

Abstract

In the present work, we investigate the decays of $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ and $B^0\to \varphi {\pi }^{+}{\pi }^{-}$ with the final state interactions based on the chiral unitary approach. In the final state interactions of the ${\pi }^{+}{\pi }^{-}$ with its coupled channels, we study the effects of the $\eta \eta$ channel in the two-body interactions for the reproduction of the $f_0(980)$ state. Our results for the ${\pi }^{+}{\pi }^{-}$ invariant mass distributions of the decay $B_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ describe the experimental data up to 1 GeV well, with the resonance contributions from the $f_0(980)$ and $\rho$. For the predicted invariant mass distributions of the $B^0\to \varphi {\pi }^{+}{\pi }^{-}$ decay, we found that the contributions from the $f_0(500)$ are significant except for the ones from the $f_0(980)$ state. With some experimental branching ratios as input to determine the production vertex factors, we make some predictions for the branching ratios of the other final decay channels, including the vector mesons, in the $B_{(s)}^0$ decays, where some of them are consistent with the experimental ones within the uncertainties.

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