Search

Motivated by the measurements of the branching fractions of the quasi-two-body decays ${B}^{0}\ensuremath{\rightarrow}{K}^{*0}({f}_{0}(980)\ensuremath{\rightarrow}){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}({f}_{0}(980)\ensuremath{\rightarrow}){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, we study the charmless $B\ensuremath{\rightarrow}V({f}_{0}(980)\ensuremath{\rightarrow}){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays in the perturbative QCD approach. Supposing that ${f}_{0}(980)$ is a two-quark state and mixture of $n\overline{n}=(u\overline{u}+d\overline{d})/\sqrt{2}$ and $s\overline{s}$ with the mixing angle $\ensuremath{\theta}$, we calculate the branching fractions of these decays with the new introduced $s$-wave ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$-pair wave function. When the mixing angle $\ensuremath{\theta}$ lies in the range $[135\ifmmode^\circ\else\textdegree\fi{},155\ifmmode^\circ\else\textdegree\fi{}]$, the calculated branching fractions of the ${B}^{0}\ensuremath{\rightarrow}{K}^{*0}{f}_{0}(980)\ensuremath{\rightarrow}{K}^{*0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{f}_{0}(980)\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays are in agreement with the experimental data. The branching fractions of other decays could be measured in the current LHCb and Belle II experiments. Considering the isospin symmetry, we also estimate the branching fractions of the quasi-two-body decays $B\ensuremath{\rightarrow}V{f}_{0}(980)\ensuremath{\rightarrow}\phantom{\rule{0ex}{0ex}}V{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, which are half of the corresponding decays $B\ensuremath{\rightarrow}V{f}_{0}(980)\ensuremath{\rightarrow}V{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. Moreover, the direct $CP$ asymmetries of these decays are also calculated, and some of them can be tested in the current experiments.

We suggest that the uncertain state ${f}_{X}(1500)$ observed by Belle and BABAR more than a decade ago, which has been viewed as a single scalar or a combination of several even spin resonances, is the vector ${\ensuremath{\rho}}^{0}(1450)$ reported recently by LHCb. Adopting the perturbative QCD approach, we determine the dikaon distribution amplitudes with the ${\ensuremath{\rho}}^{0}(1450)$ resonance from the LHCb data for the quasi-two-body decays ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$. It is then shown that the ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{+}{K}^{\ensuremath{-}}$ decay spectrum around the invariant mass $M({K}^{+}{K}^{\ensuremath{-}})\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{GeV}$ measured by BABAR can be well described by the resonant contribution from ${\ensuremath{\rho}}^{0}(1450)$. The broad structure in the ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}_{S}{K}_{S}$ spectrum around the invariant mass 1.5 GeV of a ${K}_{S}{K}_{S}$ pair, which ${\ensuremath{\rho}}^{0}(1450)$ cannot decay into because of Bose-Einstein statistics, can be accounted for by a nonresonant $S$-wave contribution alone. The branching fractions and/or the direct $CP$ asymmetries of the ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$, ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{K}^{+}{K}^{+}{K}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{K}^{0}{K}^{+}{K}^{\ensuremath{-}}$ modes are predicted, which can be tested at the ongoing LHCb and Belle-II experiments. We encourage experimental colleagues to scrutinize our postulation by analyzing relevant data with higher precision.

We investigate the ${B}_{d,s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decays in the framework of perturbative QCD (PQCD) approach with a referenced value ${\ensuremath{\phi}}_{{f}_{1}}\ensuremath{\sim}24\ifmmode^\circ\else\textdegree\fi{}$. Here, ${f}_{1}$ denotes the axial-vector mesons ${f}_{1}(1285)$ and ${f}_{1}(1420)$ with mixing angle ${\ensuremath{\phi}}_{{f}_{1}}$ in the quark-flavor basis. The observables such as branching ratios, direct $CP$ violations, and polarization fractions of the ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decays are predicted for the first time. We find that (i) the almost pure penguin modes ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ have large branching ratios in the order of ${10}^{\ensuremath{-}6}\ensuremath{\sim}{10}^{\ensuremath{-}5}$ due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{n}{f}_{s}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{s}{f}_{s}$ with ${f}_{n}$ and ${f}_{s}$ being the quark-flavor states of ${f}_{1}$ mesons. (ii) The observables receive important contributions from the weak annihilation diagrams in the PQCD approach. In particular, without the annihilation contributions, the ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}(1420){f}_{1}(1420)$ branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the ${B}_{d,s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decay rates on ${\ensuremath{\phi}}_{{f}_{1}}$ exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of ${\ensuremath{\phi}}_{{f}_{1}}$ inversely. All the PQCD predictions await for the (near) future examinations at Large Hadron Collider beauty and/or Belle-II experiments to further understand the properties of the axial-vector mesons and the perturbative dynamics released from the considered decay modes.

Recent experimental results of R(D(*)) deviate from the standard model (SM) by 3.1σ, suggesting a new physics (NP) that affects the b→cτν¯τ transition. Motivated by this, we investigate the possible NP effects in the Λb→Λcτν¯τ decay. For this purpose, assuming the neutrinos are left-handed, we calculate in detail the helicity amplitudes of Λb→Λcℓν¯ℓ (ℓ=e−, μ−, and τ−) decays with all possible four-fermion operators. Within the latest results of Λb→Λc form factors from lattice QCD calculations, we study these decays in a model-independent manner. The differential and total branching fractions, the longitudinal polarizations of final leptons and hadrons, the forward-backward asymmetries in the lepton side, the convexity parameters, and the ratio R(Λc) are calculated. In SM, we obtain the ratio R(Λc)=0.33±0.01. Supposing that NP only affects the third generation fermions, we present the correlations among R(D), R(D*), and R(Λc), as the Λb→Λcτν¯τ and B→D(*)τν¯τ are all induced by b→cℓν¯ℓ. We perform a minimum χ2 fit of the Wilson coefficient of each operator to the latest experimental data of different observables, including the ratios R(D(*)) and R(J/ψ) and the τ polarization Pτ(D*). It is found that the left-handed scalar operator OSL affects the branching fraction remarkably, and the ratio R(Λc) can be enhanced by 30%. For other operators, the ratio amounts to 0.38±0.02, which is larger than prediction of SM by 20%. Using the fitted values of the Wilson coefficients of the single NP operators, we also give a prognosis for the physical observables of Λb→Λcτν¯τ, including the ratio R(Λc), forward-backward asymmetry, and other polarized observables as well as the differential branching fraction. Furthermore, we also study the effects of three typical NP models on the ratio and the differential branching fraction of Λb→Λcτν¯τ. We hope our results can be tested in the current LHCb experiment and the future high energy experiments.

Encouraged by the global agreement between theoretical predictions and experimental measurements for $B\ensuremath{\rightarrow}J/\ensuremath{\psi}V$ decays, we extend that perturbative QCD formalism to ${B}_{d,s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(500)[{f}_{0}(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of ${f}_{0}(500)$ and ${f}_{0}(980)$. With the angle ${\ensuremath{\phi}}_{f}\ensuremath{\approx}25\ifmmode^\circ\else\textdegree\fi{}$ of the ${f}_{0}(500)\ensuremath{-}{f}_{0}(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the ${B}_{d}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(500)(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ and ${B}_{d,s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(980)(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(500)(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ one. Then, we further explore the relevant observables of the ${B}_{d,s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(500)[{f}_{0}(980)]$ decays, which could provide further constraints on the mixing angle ${\ensuremath{\phi}}_{f}$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict $\mathrm{BR}({B}_{d}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(980)(\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}))=5.{8}_{\ensuremath{-}2.9}^{+3.1}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and $\mathrm{BR}({B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{f}_{0}(980)(\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}))=4.{6}_{\ensuremath{-}2.3}^{+2.6}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. All theoretical predictions await the future examinations with high precision.

The leptonic radiative decay $B\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\ensuremath{\nu}$ is of great importance in the determination of $B$-meson wave functions, and evaluating the form factors ${F}_{V,A}$ is the essential problem on the study of this channel. We compute the next-to-leading power corrections to the form factors within the framework of PQCD approach, including the power suppressed hard kernel, the contribution from a complete set of three-particle $B$-meson wave functions up to twist-4 and two-particle off light-cone wave functions, the $1/{m}_{b}$ corrections in heavy quark effective theory (HQET), and the contribution from hadronic structure of photon. In spite of large theoretical uncertainties, the overall power suppressed contributions decreases about 50% of the leading power result. The ${\ensuremath{\lambda}}_{B}$ dependence of the integrated branching ratio is reduced after including the subleading power contributions, thus the power corrections lead to more ambiguity in the determination of ${\ensuremath{\lambda}}_{B}$ from $B\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\ell}\ensuremath{\nu}$ decay.

Two-body charmless hadronic ${B}_{c}$ decays involving a light $1{^{3}P}_{2}$-tensor ($T$) meson are investigated for the first time within the framework of perturbative QCD (pQCD) at leading order, in which the other meson is the lightest pseudoscalar ($P$) or vector ($V$) state. The concerned processes can only occur through the pure weak annihilation topology in the standard model. We predict the $CP$-averaged branching ratios and polarization fractions of those considered decays in Cabibbo-Kobayashi-Maskawa (CKM) favored and suppressed modes. Phenomenologically, several modes---such as the ${B}_{c}\ensuremath{\rightarrow}{K}_{2}^{*}(1430)K$ and the CKM-favored ${B}_{c}\ensuremath{\rightarrow}TV$---have large decay rates of ${10}^{\ensuremath{-}6}$, which are expected to be detected at Large Hadron Collider experiments in the near future. Moreover, all of the ${B}_{c}\ensuremath{\rightarrow}TV$ modes are governed by the longitudinal amplitudes in the pQCD calculations and the corresponding fractions vary around 78--98%. A confirmation of these results could prove the reliability of the pQCD approach used here and further shed some light on the annihilation decay mechanism.

Based on the assumption of two-quark structure for the light scalar mesons, within the perturbative QCD approach, we investigate the $B\ensuremath{\rightarrow}{D}^{(*)}S(q=u,d,s)$ decays induced by the $b\ensuremath{\rightarrow}u$ transition, with $S$ denoting a light scalar meson. Under two different scenarios, the branching ratios of 96 decay modes have been calculated, most of which are in the range ${10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}8}$. These results can be tested in the ongoing LHCb experiment and the forthcoming Belle-II experiment. The comparison between our predictions and the experimental data allows us to probe the inner structure of the scalar mesons. In the standard model, since all decays can only occur through tree operators, there are no $CP$ asymmetries. We note that, due to the mass difference between charm quark and light quarks, the contribution from annihilation diagrams will be enhanced sizably, especially for these color-suppressed or pure-annihilation-type decay modes. We also find that the branching ratios of color-favored decays are sensitive to the different scenarios, so their measurement will help us differentiate the different scenarios. It is also found that the ratios between $\mathrm{Br}(B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\sigma})$ and $\mathrm{Br}(B\ensuremath{\rightarrow}{D}^{(*)}{f}_{0}(980))$ can be used to determine the mixing angle of $\ensuremath{\sigma}$ and ${f}_{0}(980)$.

We investigate the branching ratios, the polarization fractions, the direct CP-violating asymmetries, and the relative phases in 20 nonleptonic decay modes of $B \to f_1 V$ within the framework of perturbative QCD approach at leading order with $f_1$ including two $^3\!P_1$-axial-vector states $f_1(1285)$ and $f_1(1420)$. Here, $B$ denotes $B^+$, $B^0$, and $B_s^0$ mesons and $V$ stands for the lightest vector mesons $\rho$, $K^*$, $\omega$, and $\phi$ , respectively. The $B_s^0 \to f_1 V$ decays are studied theoretically for the first time in the literature. Together with the angle $\phi_{f_1} \approx (24^{+3.2}_{-2.7})^\circ$ extracted from the measurement through $B_{d/s} \to J/\psi f_1(1285)$ modes for the $f_1(1285)-f_1(1420)$ mixing system, it is of great interest to find phenomenologically some modes such as the tree-dominated $B^+ \to f_1 \rho^+$ and the penguin-dominated $B^{+,0} \to f_1 K^{*+,0}, B_s^0 \to f_1 \phi$ with large branching ratios around ${\cal O}(10^{-6})$ or even ${\cal O}(10^{-5})$, which are expected measurable at the LHCb and/or the Belle-II experiments in the near future. The good agreement [sharp contrast] of branching ratios and decay pattern for $B^+ \to f_1 \rho^+, B^{+,0} \to f_1(1285) K^{*+,0} [B^{+,0} \to f_1(1420) K^{*+,0}]$ decays between QCD factorization and perturbative QCD factorization predictions can help us to distinguish these two rather different factorization approaches via precision measurements, which would also be helpful for us to explore the annihilation decay mechanism through its important roles for the considered $B \to f_1 V$ decays.

We reexamine the branching fractions, CP asymmetries, and other observables in a large number of B-q -> VV(q = u, d, s) decays in the perturbative QCD approach, where V denotes a light vector meson (rho, K*,omega, phi)The essential difference between this work and earlier similar works is of parametric origin and in the estimates of the power corrections related to the ratio r(i)(2) = m(Vi)(2)/ m(B)(2) (i = 2, 3) (m(V) and m(B) denote the masses of the vector and B meson, respectively). In particular, we use up-to-date distribution amplitudes for the final state mesons and keep the terms proportional to the ratio r(i)(2) in our calculations. Our updated calculations are in agreement with the experimental data, except for a limited number of decays which we discuss. We emphasize that the penguin annihilation and the hard- scattering emission contributions are essential to understanding the polarization anomaly, such as in the B -> phi K* and B-s -> phi phi decay modes. We also compare our results with those obtained in the QCD factorization approach and comment on the similarities and differences, which can be used to discriminate between these approaches in future experiments.

We study 20 charmless hadronic $B \to f_1 P$ decays in the perturbative QCD(pQCD) formalism with $f_1$ representing axial-vector mesons $f_1(1285)$ and $f_1(1420)$ that result from a mixing of quark-flavor $f_{1q}$ and $f_{1s}$ states with the angle $\phi_{f_1}$. The estimations of branching ratios and CP asymmetries of the considered $B \to f_1 P$ decays are presented in the pQCD approach with $\phi_{f_1} \sim 24^\circ$ from recently measured $B_{d/s} \to J/\psi f_1(1285)$ decays. It is found that (a) the tree(penguin) dominant $B^+ \to f_1 \pi^+(K^+)$ decays with large branching ratios[${\cal O}(10^{-6})$] and large direct CP violations(around 14% $\sim$ 28% in magnitude) simultaneously are believed to be clearly measurable at the LHCb and Belle II experiments; (b) the $B_d \to f_1 K_S^0$ and $B_s \to f_1 (\eta, \eta^{\prime})$ decays with nearly pure penguin contributions and safely negligible tree pollution also have large decay rates in the order of $10^{-6} \sim 10^{-5}$, which can be confronted with the experimental measurements in the near future; (c) as the alternative channels, the $B^+ \to f_1 (\pi^+, K^+)$ and $B_d \to f_1 K_S^0$ decays have the supplementary power in providing more effective constraints on the Cabibbo-Kobayashi-Maskawa weak phases $\alpha$, $\gamma$, and $\beta$ correspondingly, which are explicitly analyzed through the large decay rates and the direct and mixing-induced CP asymmetries in the pQCD approach and are expected to be stringently examined by the measurements with high precision. The complete abstraction can be found in the paper.

We investigate the CP-averaged branching ratios, the polarization fractions, the relative phases, and the CP-violating asymmetries of the penguin-dominated $B \to \phi K_1(1270) $ and $ \phi K_1(1400)$ decays in the perturbative QCD(pQCD) approach, where $K_1(1270)$ and $K_1(1400)$ are believed to be the mixtures of two distinct types of axial-vector $K_{1A}(^3P_1)$ and $K_{1B}(^1P_1)$ states with different behavior, however, their mixing angle $\theta_{K_1}$ is still a hot and controversial topic presently. By numerical evaluations with two different mixing angles $\theta_{K_1} \sim 33^\circ$ and $58^\circ$ and phenomenological analysis, we find that: (a) the pQCD predictions for the branching ratio, the longitudinal polarization fraction and the direct CP violation of $B^\pm \to \phi K_1(1270)^\pm$ decay with the smaller angle $33^\circ$ are in good agreement with the currently available data; (b) though the central values significantly exceed the available upper limit, both pQCD predictions of $Br(B^\pm \to \phi K_1(1400)^\pm)$ with two different mixing angles are consistent with that obtained in QCD factorization and with the preliminary data in 2$\sigma$ errors. These results and other relevant predictions for the considered decays will be further tested by the LHCb and the forthcoming Super-B experiments; (c) the weak annihilation contributions can play an important role in $B \to \phi K_1(1270)$ and $\phi K_1(1400)$ decays; (d) these pQCD predictions combined with the future precision measurements can examine the reliability of the factorization approach employed here, but also explore the complicated QCD dynamics and mixing angle $\theta_{K_1}$ of the axial-vector $K_1(1270)$ and $K_1(1400)$ system.

We investigate $B\ensuremath{\rightarrow}{K}_{0}^{*}(1430){K}^{*}$ decays in the perturbative QCD (pQCD) factorization approach, where $B$ denotes ${B}_{u}$, ${B}_{d}$, and ${B}_{s}$ mesons, respectively, and the scalar ${K}_{0}^{*}(1430)$ is considered as a meson based on the model of the conventional two-quark structure. With the light-cone distribution amplitude of ${K}_{0}^{*}(1430)$ defined in two scenarios, namely Scenario 1 and Scenario 2, we make the first estimation for the branching ratios and $CP$-violating asymmetries for those concerned decay modes in the pQCD factorization approach. For all considered $B\ensuremath{\rightarrow}{K}_{0}^{*}(1430){K}^{*}$ decays in this paper, only one preliminary upper limit on the branching ratio of ${B}^{0}\ensuremath{\rightarrow}{K}_{0}^{*}(1430{)}^{0}{\overline{K}}^{*0}$ measured at 90% C.L. by the Belle Collaboration is available now. It is therefore of great interest to examine the predicted physical quantities at two $B$ factories, the Large Hadron Collider experiments, and the forthcoming Super-$B$ facility, and then to test the reliability of the pQCD approach employed to study the considered decay modes involving a $p$-wave scalar meson as one of the final state mesons. Furthermore, these pQCD predictions combined with the future precision measurements are also helpful to explore the complicated QCD dynamics involved in the light scalars.

We study the decay modes of ${B}_{s}^{0}({\overline{B}}_{s}^{0})\ensuremath{\rightarrow}{D}_{s}^{\ifmmode\pm\else\textpm\fi{}}{K}^{\ensuremath{\mp}}$, ${B}_{s}^{0}({\overline{B}}_{s}^{0})\ensuremath{\rightarrow}{D}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$, and ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{D}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ in the perturbative QCD approach based on ${k}_{T}$ factorization, including the branching ratios and $CP$ violation parameters which provide a clear way to extract the Cabibbo-Kobayashi-Maskawa angle $\ensuremath{\gamma}$. Our results of branching ratios of ${B}_{s}^{0}({\overline{B}}_{s}^{0})\ensuremath{\rightarrow}{D}_{s}^{\ifmmode\pm\else\textpm\fi{}}{K}^{\ensuremath{\mp}}$ and ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{D}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ and the $CP$ asymmetry of ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{D}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ agree well with the experimental data. We also give predictions of the other observables, which provide some guidance for experiments in the future, especially for the LHCb experiment.

We study the double charm decays of ${B}_{c}$ meson, by employing the perturbative QCD approach based on ${k}_{T}$ factorization. In this approach, we include the nonfactorizable emission diagrams and W annihilation diagrams, which are neglected in the previous naive factorization approach. The former are important in the color-suppressed modes, while the latter are important in most ${B}_{c}$ decay channels owing to the large Cabibbo-Kobayashi-Maskawa matrix elements. We make a comparison with those previous naive factorization results for the branching ratios and also give out the theoretical errors that were previously missed. We predict the transverse polarization fractions of ${B}_{c}\ensuremath{\rightarrow}{D}_{(s)}^{*+}{\overline{D}}^{*0}$, ${D}_{(s)}^{*+}{D}^{*0}$ decays for the first time. A large transverse polarization contribution that can reach 50%--60% is predicted in some of the ${B}_{c}$ meson decays.

We make a systematic investigation on the two-body nonleptonic decays B-c -> D-(s)(()*P-), D-(s)(()*V-), by employing the perturbative QCD approach based on k(T) factorization, where P and V denote any light pseudoscalar meson and vector meson, respectively. We predict the branching ratios and direct CP asymmetries of these B-c decays and also the transverse polarization fractions of B-c -> D*V-(s) decays. It is found that the nonfactorizable emission diagrams and annihilation-type diagrams have remarkable effects on the physical observables in many channels, especially the color-suppressed and annihilation-dominant decay modes. A possible large direct CP violation is predicted in some channels; and a large transverse polarization contribution which can reach 50% similar to 70% is predicted in some of the B-c -> D*V-(s) decays.