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

Abstract

We analyzed the nonleptonic decays $B/B_s\to \psi (2S)V$ with $V=(\rho ,\omega ,K^{\ast },\varphi )$ 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 nonfactorizable 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 $B_{(s)}\to \psi (2S)K^{\ast },\psi (2S)\varphi$ decays are consistent with the measured values within errors. As for $B\to \psi (2S)\rho ,\psi (2S)\omega$ 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 $CP$ 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 $\sin 2{\beta }_{(s)}$, which suggests that these channels can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa (CKM) angle $\beta$ and ${\beta }_s$. We found that the longitudinal polarization fractions $f_0$ are suppressed to $\sim 50\%$ due to the large nonfactorizable contributions. The magnitudes and phases of the two transverse amplitudes ${\mathcal{A}}_{\parallel }$ and ${\mathcal{A}}_{\perp }$ are roughly equal, which is an indication for the approximate light quark helicity conservation in these decays. The overall polarization observables of $B\to \psi (2S)K^{\ast 0}$ and $B_s\to \psi (2S)\varphi$ 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.

Comments: 14 pages, 1 figure, 6 tables