Three-Body $B^0_{(s)}$ to $\phi \pi^+ \pi^-$ Decays

We interest to investigate of the three-body decays of $B^{0}$ meson to $\phi\pi^+\pi^-$ and $B_s^{0}$ meson to $\phi \pi^{+}\pi^{-}$. Hadronic three-body decays include both nonresonant and resonant contributions, on the basis of the factorization hypothesis. In this analysis, resonant structure is exhibited only in the $\pi^+\pi^-$ channel which the resonant contribution can be described by S-wave, P-wave and D-wave $\pi^+\pi^-$ contribution from $f_0(980)$, $\rho$ and $f_2$ mesons and other possible resonance. Therefore, the theoretical values at the scale $m_b$ are $(1.69 \pm 0.19 )\times10^{-7}$ and $(3.28\pm 0.17 )\times10^{-6}$, while the experimental results of them are $(1.82 \pm 0.25 )\times10^{-7}$ and $(3.48\pm 0.23 )\times10^{-6}$, respectively. Comparing computation analysis values with experimental values show that our results at the scale $\mu_b$ are in agreement with them.