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

TL;DR

This paper investigates the decay processes of B mesons into phi and pion pairs, analyzing resonant structures and comparing theoretical predictions with experimental data, confirming the validity of the factorization hypothesis.

Contribution

The study provides a detailed analysis of resonant contributions in three-body B meson decays, incorporating multiple resonance channels and validating theoretical models against experimental results.

Findings

Theoretical decay rates agree with experimental measurements.

Resonant structures include f0(980), rho, and f2 mesons.

Analysis supports the factorization hypothesis in these decays.

Abstract

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.