Branching ratios, CP asymmetries and polarizations of $$B\rightarrow \psi (2S) V$$ B → ψ ( 2 S ) V decays

Abstract We analyze the non-leptonic decays $$B/B_s\rightarrow \psi (2S) V $$ B / B s → ψ ( 2 S ) V with $$V=(\rho , \omega , K^{*}, \phi )$$ V = ( ρ , ω , K ∗ , ϕ ) by employing the perturbative QCD (pQCD) factorization approach. Here the branching ratios, the CP 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 $$B_{(s)}\rightarrow \psi (2S)K^{*}, \psi (2S)\phi $$ B ( s ) → ψ ( 2 S ) K ∗ , ψ ( 2 S ) ϕ decays are consistent with the measured values within errors. As for $$B\rightarrow \psi (2S) \rho , \psi (2S) \omega $$ B → ψ ( 2 S ) ρ , ψ ( 2 S ) ω decays, the branching ratios can reach the order of $$10^{-5}$$ 10 - 5 and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct CP asymmetries of the considered decays are very small. Thus the observation of any large direct CP asymmetry for these decays will be a signal for new physics. The mixing-induced CP asymmetries in the neutral modes are very close to $$\sin 2\beta _{(s)}$$ sin 2 β ( s ) , which suggests that these channels can give a cross-check on the measurement of the Cabbibo–Kobayashi–Maskawa (CKM) angle $$\beta $$ β and $$\beta _s$$ β s . We find that the longitudinal polarization fractions $$f_0$$ f 0 are suppressed to $$\sim 50\%$$ ∼ 50 % due to the large non-factorizable contributions. The magnitudes and phases of the two transverse amplitudes $$\mathcal {A}_{\parallel }$$ A ‖ and $$\mathcal {A}_{\perp }$$ A ⊥ are roughly equal, which is an indication for the approximate light-quark helicity conservation in these decays. The overall polarization observables of $$B\rightarrow \psi (2S) K^{*0}$$ B → ψ ( 2 S ) K ∗ 0 and $$B_s\rightarrow \psi (2S) \phi $$ 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