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Branching ratios, C P asymmetries and polarizations of B → ψ( 2 S ) V decays

We analyze the non-leptonic decays B / B s → ψ( 2 S ) V with V = (ρ, ω, K ∗ , φ) by employing the perturbative QCD (pQCD) factorization approach. Here the branching ratios, the C P asymmetries and the complete set of polarization observables are investigated systematically. Besides the traditional contributions from the factorizable and non-factorizable diagrams at the leading order, the next-to-leading order (NLO) vertex corrections could also provide considerable contributions. The pQCD predictions for the branching ratios of the B ( s ) → ψ( 2 S ) K ∗ , ψ( 2 S )φ decays are consistent with the measured values within errors. As for B → ψ( 2 S )ρ, ψ( 2 S )ω decays, the branching ratios can reach the order of 10 − 5 and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct C P asymmetries of the considered decays are very small. Thus the observation of any large direct C P asymmetry for these decays will be a signal for new physics. The mixing-induced C P asymmetries in the neutral modes are very close to sin 2 β ( s ) , which suggests that these channels can give a cross-check on the measurement of the Cabbibo–Kobayashi–Maskawa (CKM) angle β and β s . We ﬁnd that the longitudinal polarization fractions f 0 are suppressed to ∼ 50% due to the large non-factorizable contributions. The magnitudes and phases of the two transverse amplitudes A (cid:5) and A ⊥ are roughly equal, which is an indication for the approximate light-quark helicity conservation in these decays. The overall polarization observables of B → ψ( 2 S ) K ∗ 0 and B s → ψ( 2 S )φ channels are also in good agreement with the experimental measurements as reported by LHCb and BaBar. Other results can also be tested by the LHCb and Belle-II experiments.