In this work, we study the ($S$, $P$ and $D$)-wave $K^+K^-$ contributions to $B\to KKK$ decays in the perturbative QCD approach at leading order. Within the two-meson wave functions describing the nonperturbative dynamics in the kaon-pair for different waves, we calculate the branching fractions and the direct $CP$ asymmetries of these decay modes in the corresponding resonance regions. Most of our numerical results are well consistent with the current measurements. We note that the narrow-width approximation is invalid in the quasi-two-body decays $B\to Kf_0(980)\to KKK$. For other decays, under the narrow-width approximation we can extract the branching fractions of the corresponding two-body decays involving the intermediate resonant states, and the related branching fractions agree with the current experimental data well. Furthermore, we also predict the corresponding quasi-two-body decays $B\to Kπ^+π^-$, which are expected to be measured in the ongoing LHCb and Belle-II experiments.
In this work, we study the $S$, $P$ and $D$ wave resonance contributions to three-body decays $B_{(s)} \to [ D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ by employing the perturbative QCD (PQCD) approach, where the kaon-kaon invariant mass spectra are dominated by the $f_0(980),f_0(1370),$ $ϕ(1020),ϕ(1680),f_2(1270),f^{\prime}_2(1525),f_2(1750)$ and $f_2(1950)$ resonances. The $KK$ $S$-wave component $f_0(980)$ is modeled with the Flatté formalism, while other resonances are described by the relativistic Breit-Wigner (BW) line shape. The corresponding decay channels are studied by constructing the kaon-ka…
We extend our recent works on the $P$-wave two-pion resonant contributions to the kaon-pion cases in the hadronic charmless $B$ meson decays by employing the perturbative QCD approach. The concerned decay modes are analysed in the quasi-two-body framework by parameterizing the kaon-pion distribution amplitude $Φ_{K π}^{\rm P}$, which contains the final state interactions between the kaon and pion in the resonant region. The relativistic Breit-Wigner formula for the $P$-wave resonant state $K^*(892)$ is adopted to parameterize the time-like form factor $F_{Kπ}$. We calculate the $CP$-averaged b…
Intense field quantum field theory (IFQFT) is used to determine new phenomenological predictions arising from Compton scattering and pair production in a strong laser field. This theory utilizes exact solutions of fermions embedded in external plane waves which carry over to a strong field fermion propagator. When these strong field fermions also interact with probe photons, the transition probability is enhanced in a series of resonances when the kinematics allow the virtual fermion to go on-shell. An analysis of parameters shows that contemporary experiments could already produce these predi…
Three-body $B$ decays not only significantly broaden the study of $B$ meson decay mechanisms, but also provide information of resonant particles. Because of complicate dynamics, it is very hard for us to study the whole phase space in a specific approach. In this review, we take $B\to K({\cal R}\to) K^+K^-$ decays as examples and show the application of the perturbative QCD (PQCD) approach in studying the quasi-two-body $B$ decays, where two particles move collinearly with large energy and the bachelor one recoils back. To describe the dynamics of two collinear particles, the ($S$, $P$ and $D$…
We analyze the quasi-two-body decays $B\to Kρ\to Kππ$ in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the $P$-wave states $ρ(770)$ and $ρ^\prime(1450)$ are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct $CP$ asymmetries of the $B\to Kρ(770),Kρ^\prime(1450)\to Kππ$ modes. It is shown that agreement of theoretical results with data can be achieved, through whi…
In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P f_2(1270)\to Pππ$ with the two-pion distribution amplitude $Φ_{ππ}^{\rm D}$ by using the perturbative QCD factorization approach, where $P$ represents a light pseudoscalar meson $K, π, η$ and $η^{\prime}$. The relativistic Breit-Wigner formula for the $D$-wave resonance $f_2(1270)$ 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 theoretic…
We extend our recent works on the two-pion $S$-wave resonance contributions to the kaon-pion ones in the $B$ meson hadronic charmonium decay modes based on the perturbative QCD approach. The $S$-wave $Kπ$ time-like form factor in its distribution amplitudes is described by the LASS parametrization, which consists of the $K^*_0(1430)$ resonant state together with an effective range nonresonant component. The predictions for the decays $B\rightarrow J/ψKπ$ in this work agree well with the experimental results from $BABAR$ and Belle Collaborations. We also discuss theoretical uncertainties, indic…
In this paper, we studied the $B_{(s)} \to (D_{(s)},\bar{D}_{(s)}) ρ\to (D_{(s)}, \bar{D}_{(s)})ππ$ decays by employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach. We use the two-pion distribution amplitudes $Φ_{ππ}$, which contains both resonant and nonresonant contributions from the pion pair, to describe the final state interactions (FSIs) between the pions in the resonant region. We found that (a) for all considered decays, the PQCD predictions for their branching ratios based on the quasi-two-body and the two-body framework agree well w…
In this note, we study the contributions from the S-wave resonances, f_{0}(980) and f_{0}(1500), to the B^{0}_{s}\rightarrow ψ(3770)π^ {+}π^{-} decay by introducing the S-wave ππdistribution amplitudes within the framework of the perturbative QCD approach. Both resonant and nonresonant contributions are contained in the scalar form factor in the S-wave distribution amplitude Φ^S_{ππ}. Since the vector charmonium meson ψ(3770) is a S-D wave mixed state, we calculated the branching ratios of S-wave and D-wave respectively, and the results indicate that f_{0}(980) is the main contribution of the …
We present a comprehensive study of the production of top quark pairs in association with one hard jet in the di-lepton decay channel at the LHC. Our predictions, accurate at NLO in QCD, focus on the LHC Run II with a center-of-mass energy of 13 TeV. All resonant and non-resonant contributions at the perturbative order ${\cal O}(α_s^4 α^4)$ are taken into account, including irreducible backgrounds to $t\bar{t}j$ production, interferences and off-shell effects of the top quark and the $W$ gauge boson. We extensively investigate the dependence of our results upon variation of renormalisation and…
In this work, we studied the quasi-two-body decays $B_{(s)} \to ψ[K^*(892), K^*(1410),$ $K^*(1680)] \to ψKπ$ by employing the perturbative QCD (PQCD) factorization approach, where the charmonia $ψ$ represents $J/ψ$ and $ψ(2S)$. The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude (DA) $Φ_{K π}^{\rm P}$, which contained the important final state interactions between the kaon and pion in the resonant region. The relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor $F_{Kπ}$ appeared in the kaon-pion DAs. The SU(3) fl…
