A model-independent analysis of final-state interactions in B ¯ d / s 0 → J / ψ π π $$ {\overline{B}}_{d/s}^0\to J/\psi \pi \pi $$

Abstract

Exploiting B-meson decays for Standard Model tests and beyond requires a precise understanding of the strong final-state interactions that can be provided modelindependently by means of dispersion theory. This formalism allows one to deduce the universal pion-pion final-state interactions from the accurately known ππ phase shifts and, in the scalar sector, a coupled-channel treatment with the kaon-antikaon system. In this work an analysis of the decaysB 0 d → J/ψπ + π − andB 0 s → J/ψπ + π − is presented. We find very good agreement with the data up to 1.05 GeV in the ππ invariant mass, with a number of parameters reduced significantly compared to a phenomenological analysis. In addition, the phases of the amplitudes are correct by construction, a crucial feature for many CP violation measurements in heavy-meson decays.

B meson weak decays to J/ψ − f0(500) (f0(980), ρ, ω, ϕ)

“…The decaysB 0 d → J/ψπ + π − andB 0 s → J/ψπ + π − have been analysed using form factors, computed with the Omnes method. They have been found to be in very good agreement with the data up to 1.05 GeV [16].…”

The branching ratio $$\omega \rightarrow \pi ^+\pi ^-$$ ω → π + π - revisited

“…Similar ansätze for the ρ-ω mixing term were used before frequently [10,12,13,[27][28][29]; we employ the sign convention of Ref. [29]. We checked that the results extracted from the pion vector form factor using Eqs.…”

“…Besides aiming for a further improvement in the statistical precision of the determination of this quantity, we may find further, systematically independent justification for our conclusion on the data selection in the average, namely the omission of the BaBar results. One future option could be the decayB 0 d → J/ψπ + π − , where the mixing signal shows up very prominently [29]. However, the data presently available in this channel [41] are insufficient for a quantitative analysis.…”

$$\Lambda _b \rightarrow \pi ^- (D_s^-) \Lambda _c(2595),~\pi ^- (D_s^-) \Lambda _c(2625)$$ Λ b → π - ( D s - ) Λ c ( 2595 ) , π - ( D s - ) Λ c ( 2625 ) decays and $$DN,~D^*N$$ D N , D ∗ N molecular components

“…[5], where f 0 (500) and f 0 (980) appear as a consequence of the pseudoscalar meson-pseudoscalar meson interaction in coupled channels [6], using dynamics from the chiral Lagrangians [7]. The same idea, with a different formalism, has been applied later with the same conclusions [8,9].…”