In this work, we calculate the $CP$-averaged branching ratios and the direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P(\rho \to )\pi \pi$ by employing the perturbative QCD (PQCD) approach (here $P$ stands for a light pseudoscalar meson $\pi$, $K$, $\eta$ or ${\eta }^{\prime }$). The vector current timelike form factor $F_{\pi }$, which contains the final-state interactions between the pion pair in the resonant region associated with the $P$-wave states $\rho (770)$ along with the two-pion distribution amplitudes, is employed to describe the interactions between the $\rho$ and the pion pair under the hypothesis of the conserved vector current. We found that (a) the PQCD predictions for the branching ratios and the direct $CP$-violating asymmetries for most considered $B_{(s)}\to P(\rho \to )\pi \pi$ decays agree with currently available data within errors, (b) for $\mathcal{B}(B\to {\pi }^0{\rho }^0\to {\pi }^0({\pi }^{+}{\pi }^{-})$, the PQCD prediction is much smaller than the measured one, and (c) for the $B^{+}\to {\pi }^{+}({\rho }^0\to ){\pi }^{+}{\pi }^{-}$ decay mode, there is a negative $CP$ asymmetry $({-27.5}_{-3.7}^{+3.0})\%$, which agrees with other theoretical predictions but is different in sign from those reported by the BABAR and LHCb Collaborations.

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ by employing the perturbative QCD (PQCD) factorization approach, where $P$ is a light pseudoscalar meson $K$, $\pi$, $\eta$, and ${\eta }^{\prime }$. The considered decay modes are studied in the quasi-two-body framework by parametrizing the two-pion distribution amplitude ${\mathrm{\Phi }}_{\pi \pi }^{\mathrm{P}}$. The $P$-wave timelike form factor $F_{\pi }$ in the resonant regions associated with the ${\rho }^{\prime }(1450)$ and ${\rho }^{\prime \prime }(1700)$ is estimated based on available experimental data. The PQCD predictions for the $CP$-averaged branching ratios of the decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ are in the order of ${10}^{-7}-{10}^{-9}$. The branching ratios of the two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)$ are extracted from the corresponding quasi-two-body decay modes. The whole pattern of the squared pion form factor $|F_{\pi }{|}^2$ measured by BABAR Collaboration could also be understood based on our studies. The PQCD predictions in this work will be tested by the precise data from the LHCb and the future Belle II experiments.

We investigate the four-body decays B_(s) → (Kπ)_S/P(Kπ)_S/P in the Kπ-pair invariant mass region around the K^*(892) resonance in the perturbative QCD (PQCD) approach, where (Kπ)_S/P denotes a S- or P-wave Kπ configuration. The contributions from the P-wave resonance K^*(892) and from possible S-wave components are included into the parametrization of the Kπ two-meson distribution amplitudes, which are the non-perturbative inputs in this formalism. We calculate the branching ratio for each resonance and observe sizable S-wave contributions to the B_s modes, well consistent with recently available LHCb data. We also deduce the polarization fractions for the $$ {K}^{\ast }{\overline{K}}^{\ast } $$K ∗ K ¯ ∗ final states, and compare our predictions to those in previous PQCD analyses of the corresponding two-body B → $$ {K}^{\ast }{\overline{K}}^{\ast } $$K ∗ K ¯ ∗ decays. The polarization puzzle associated with the two U-spin related channels B⁰ → $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$K ∗ 0 K ¯ ∗ 0 and $$ {B}_s^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$B s 0 → K ∗ 0 K ¯ ∗ 0 still exists. In addition to direct CP asymmetries, triple-product asymmetries and S-wave induced direct CP asymmetries originating from the interference among various helicity amplitudes, are presented. It is shown that true triple-product asymmetries are rather small, while direct CP asymmetries and S-wave-induced direct CP asymmetries are significant in some decays. Our results will be subject to stringent tests with precise data from B factories in the near future.

We reanalyze the $$\Lambda _b\rightarrow p$$Λ b → p transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $$\Lambda _b$$Λ b baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $$\Lambda _b$$Λ b baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 $$\Lambda _b$$Λ b baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays $$\Lambda _b\rightarrow p\ell {\bar{\nu }}_\ell $$Λ b → p ℓ ν ¯ ℓ and the hadronic decay $$\Lambda _b\rightarrow p\pi $$Λ b → p π are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.

By employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach, we calculate the branching ratios of the decays $B_{(s)}\to D(\rho (1450)$, $\rho (1700))\to D\pi \pi$ with $D=(D_{(s)},{\overline{D}}_{(s)})$. The pion vector form factor $F_{\pi }$, acquired from a BABAR Collaboration analysis of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ data, is involved in the two-pion distribution amplitudes ${\mathrm{\Phi }}_{\pi \pi }^{I=1}$. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of ${10}^{-10}–{10}^{-4}$. The PQCD predictions for $\mathcal{B}(B^0\to {\overline{D}}^0({\rho }^0(1450),{\rho }^0(1700))\to {\overline{D}}^0{\pi }^{+}{\pi }^{-})$ agree well with the measured values as reported by LHCb if one takes still large theoretical errors into account. Unlike the traditional way of the PQCD approach, one can extract the decay rates for the two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))$ from the results of the corresponding quasi-two-body decays. The PQCD predictions for $\mathcal{B}(B_{(s)}\to D\rho (1450))$ and $\mathcal{B}(B_{(s)}\to D\rho (770))$ are similar in magnitude: an interesting relation to be tested by future experimental measurements.

We present the differential branching fractions for the $B\to \psi \pi \pi$ decays with the charmonia $\psi =J/\psi ,\psi (2S)$ 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 $\rho$ 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 $B\to J/\psi \pi \pi$ decays. Our predictions for the $B\to \psi (2S)\pi \pi$ 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.