Three-Body $B_{(s)}^0$ to $\varphi {\pi }^{+}{\pi }^{-}$ Decays

Abstract

We interest to investigate of the three-body decays of $B^0$ meson to $\varphi {\pi }^{+}{\pi }^{-}$ and $B_s^0$ meson to $\varphi {\pi }^{+}{\pi }^{-}$. 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 $(1.69\pm 0.19)\times 10^{-7}$ and $(3.28\pm 0.17)\times 10^{-6}$, while the experimental results of them are $(1.82\pm 0.25)\times 10^{-7}$ and $(3.48\pm 0.23)\times 10^{-6}$, respectively. Comparing computation analysis values with experimental values show that our results at the scale ${\mu }_b$ are in agreement with them.

Comments: 14 pages, 3 figures, accepted in Progress of Theoretical and Experimental Physics