Abstract
In the present work, we investigate the decays of B^{0}_{(s)} rightarrow phi pi ^{+}pi ^{-} with the final state interaction based on the chiral unitary approach. In the final state interaction of the pi ^+pi ^- with its coupled channels, we study the effects of the eta eta channel in the two-body interaction for the reproduction of the f_{0}(980) state, where its contribution to the f_{0}(980) state can be ignored. Our results for the pi ^+pi ^- invariant mass distributions of the decay B^{0}_{s} rightarrow phi 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} rightarrow phi pi ^{+}pi ^{-} decay, we find that the contributions from the f_{0}(500) are significant, but not from the 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)} decays, some of which are consistent with the experimental measurements within the uncertainties.
Highlights
The three body B meson decays have caught much attention of both theories and experiments to investigate the C Pviolation phenomena or the physics beyond the Standard Model (SM)
In order to examine the resonant contributions and understanding the production of f0(500) and f0(980) in the final state interaction, we study the decays of B(0s) → φπ +π − with the final state interaction taken from the chiral unitary approach (ChUA) as done in Refs. [44,45,46], where the B(0s) mesons decaying to J/ψ with π +π − and the other final states were investigated
We show the results of the π π invariant mass distributions for the decay of Bs0 → φπ +π − in Fig. 6, which is only plotted up to 1.1 GeV within the effective energy range of the ChUA for the meson-meson interaction [47]
Summary
Aiming at searching for the physics beyond the SM, the LHCb collaboration has reported the first observation of the rare three body decays of B(0s) → φπ +π − [53],1 where the Bs0 → φπ +π − decay was investigated for the π +π − invariant mass in the range of 400 MeV < m(ππ) < 1600 MeV, and the resonant contributions from the states of ρ(770), f0(980), f2(1270), and f0(1500), were found in the m(π π ) invariant mass distributions. The decays of B(0s) → φπ +π − are interesting because they are induced by the flavor changing neutral current [54] b → sss and b → dss processes at the quark level, which are forbidden at tree level diagram by the Cabibbo-Kobayashi-Maskawa (CKM) quarkmixing mechanism of the SM [55] These decays are sensitive to the new physics beyond the SM because their amplitudes are described by the loop (penguin) diagrams [56]. In order to examine the resonant contributions and understanding the production of f0(500) and f0(980) in the final state interaction, we study the decays of B(0s) → φπ +π − with the final state interaction taken from the ChUA as done in Refs. We will briefly introduce the formalism of the final state interaction with the ChUA for these decay processes of the B(0s) mesons.
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