We make a systematic investigation on the two-body nonleptonic decays B c → J=Ψðη c Þ; M by employing the perturbative QCD approach based on k T factorization, where M is a light pseudoscalar or vector or a heavy charmed meson. We predict the branching ratios and direct CP asymmetries of these B c decays and also the transverse polarization fractions of B c → J=ΨV; J=ψD Ã ðsÞ decays. It is found that these decays have a large branching ratios of the order of 10 −4 − 10 −2 and could be measured by the future LHCb experiment. Our predictions for the ratios of branching fractions c →J=Ψπ þ Þ are in good agreement with the data. A large transverse polarization fraction which can reach 48% is predicted in B þ c → J=ΨD Ãþ s decay, which is consistent with the data. We find a possible direct CP violation in B c → J=ψD Ã decays, which are helpful to test the CP violating effects in B c decays.

Inspired by the recent measurement of the ratio of B c branching fractions to J/ψπ + and J/ψμ + ν μ final states at the LHCb detector, we study the semileptonic decays of B c meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions B c → P, V , where P and V denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for the B c meson. It is found that the predicted branching ratios range from 10 −7 up to 10 −2 and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractionsis in good agreement with the data. For B c → V lν l decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.

Nonleptonic two-body B c decays including radially excited ψ(2S) or η c (2S) mesons in the final state are studied using the perturbative QCD approach based on k T factorization. The charmonium distribution amplitudes are extracted from the n = 2, l = 0 Schrödinger states for the harmonic oscillator potential. Utilizing these distribution amplitudes, we calculate the numerical results of the B c → ψ(2S), η c (2S) transition form factors and branching fractions of B c → ψ(2S)π, η c (2S)π decays. The ratio between two decay modes B c → ψ(2S)π and B c → J/ψπis compatible with the experimental data within uncertainties, which indicates that the harmonic-oscillator wave functions for ψ(2S) and η c (2S) work well. It is found that the branching fraction of B c → η c (2S)π , which is dominated by the twist-3 charmonium distribution amplitude, can reach the order of 10 −3 . We hope it can be measured soon in the LHCb experiment.

We present the differential branching fractions for the B → ψππ decays with the charmonia ψ = J/ψ, ψ(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 timelike form factors, normalizing the two-pion DAs, contain contributions from the ρ resonance and radial excitations fitted to the BABAR e + e − annihilation 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 → J/ψππ decays. Our predictions for the B → ψ(2S)ππ 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.

In this work, we calculate the CP-averaged branching ratios and direct CP-violating asymmetries of the quasi-two-body decays B ðsÞ → Pf 2 ð1270Þ → Pππ with the two-pion distribution amplitude Φ D ππ by using the perturbative QCD factorization approach, where P represents a light pseudoscalar meson K, π, η and η 0. The relativistic Breit-Wigner formula for the D-wave resonance f 2 ð1270Þ is adopted to parameterize the timelike form factor F π , which contains the final state interactions between the pions in the resonant regions. The consistency of theoretical results with data can be achieved by determining the Gegenbauer moments of the D-wave two-pion distribution amplitudes. The decay rates for the considered decay modes are generally in the order of 10 −9 to 10 −6. The integrated direct CP asymmetries for the charged modes agree with the BABAR and Belle measurements. As a by-product, we extract the branching ratios of B ðsÞ → Pf 2 ð1270Þ from the corresponding quasi-two-body decay modes, which still need experimental tests at the ongoing and forthcoming experiments.