Abstract
We present the differential branching fractions for the $B\rightarrow \psi \pi\pi$ decays with the charmonia $\psi=J/\psi,\psi(2S)$ in the invariant mass of the $P$-wave pion pairs in the perturbative QCD approach. The two-pion distribution amplitudes (DAs) corresponding to both longitudinal and transverse polarizations are constructed to capture important final state interactions in the processes. The time-like form factors, normalizing the two-pion DAs, contains contributions from the $\rho$ resonance and radial excitations fitted to the BaBar data. Given the hadronic parameters for the two-pion DAs associated with the longitudinal polarization which were determined in our previous study, and tuning those associated with the transverse polarization, we accommodate well the observed branching ratios and polarization fractions of the $B\rightarrow J/\psi \pi\pi$ decays. Our predictions for the $B\rightarrow \psi(2S) \pi\pi$ modes from the same set of parameters can be tested in future LHCb and BelleII experiments. We also investigate the sources of theoretical uncertainties in our calculation.
Highlights
The BðsÞ meson decay chains with charmonia and pion pairs in final states, providing rich opportunities to search for intermediate resonances, have caught both experimental and theoretical attention
Recent LHCb data [3,4] have indicated that the B → J=ψπþπ− decay spectrum is well described by six resonances in the πþπ− channel, f0ð500Þ, ρð770Þ, ρð1450Þ, ρð1700Þ, ωð782Þ
Final state interactions in the BðsÞ → J=ψππ decays were extracted from data in a framework based on dispersion theory [11]
Summary
The BðsÞ meson decay chains with charmonia and pion pairs in final states, providing rich opportunities to search for intermediate resonances, have caught both experimental and theoretical attention. Final state interactions in the BðsÞ → J=ψππ decays were extracted from data in a framework based on dispersion theory [11] These works mainly focus on the ρð770Þ contribution to the P-wave dipion system, with the two radial excitations ρð1450Þ and ρð1700Þ and the ρ-ω interference being neglected. Several collaborations [13,14] have successfully fitted the eþe− → πþπ− cross section in the vicinity of the ρð770Þ resonance, with a small but clearly visible ω-meson admixture It has been argued [15] that the dominant kinematic region for three-body B meson decays is restricted to the edges of a Dalitz plot, where two of the three final state mesons form a collimated pair in the rest frame of the B meson. The factorization formulas for the considered decay amplitudes are collected in the Appendix
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