In this paper we study the semileptonic decays of B + c → D(s) (l + ν l , l + l − , νν) (here l stands for e, µ, or τ ). After evaluating the B + c → (D (s) , D * (s) ) transition form factors F 0,+,T (q 2 ) and V (q 2 ), A 0,1,2 (q 2 ), T 1,2,3 (q 2 ) by employing the perturbative QCD factorization approach, we calculate the branching ratios for all these semileptonic decays. Our predictions for the values of the B + c → D (s) and B + c → D * (s) transition form factors are consistent with those obtained by using other methods. The branching ratios of the decay modes withνν are almost an order of magnitude larger than the corresponding decays with l + l − after the summation over the three neutrino generations. The branching ratios for the decays with b → d transitions are much smaller than those decays with the b → s transitions, due to the Cabibbo-Kobayashi-Maskawa suppression. We define ratios R D and R D * for the branching ratios with the τ lepton versus µ, e lepton final states to cancel the uncertainties of the form factors, which could possibly be tested in the near future.

We analyze the quasi-two-body decays B → Kρ → 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 ′ (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 → Kρ(770), Kρ ′ (1450) → Kππ modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the P -wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the B → Kρ(770) → Kππ decays supports the PQCD factorization framework for exclusive hadronic B meson decays. PACS numbers: 13.20.He, 13.25.Hw, 13.30.Eg I. INTRODUCTIONStrong dynamics contained in three-body hadronic B meson decays is much more complicated than in two-body cases, because of entangled nonresonant and resonant contributions, and significant final-state interactions [1]. Nonresonant contributions may not be negligible in these decays, as indicated by the observations made in Refs [2-7]. Quasi-two-body channels through intermediate scalar, vector and tensor resonances, which produce hadron pairs with final-state interactions, usually dominate total branching fractions. An amplitude for a three-body hadronic B meson decay, as a coherent sum of nonresonant and resonant contributions, leads to nonuniform distributions of events described by differential branching fractions [2-16] and of direct CP asymmetries [17][18][19][20] in a Dalitz plot [21]. Dalitzplot analyses of abundant three-body hadronic B meson decays from different collaborations (11)(12)(13)(14)(15)(16), Belle [5,6,[8][9][10] and LHCb [17][18][19]) have revealed valuable information on involved strong and weak dynamics.On the theoretical side, substantial progress on three-body hadronic B meson decays by means of symmetry principles and factorization theorems has been made, although rigorous justification of these approaches is not yet available. Isospin, U-spin and flavor SU(3) symmetries were adopted in [22][23][24][25][26][27][28][29][30][31], and the role of the CP T invariance in three-body B meson decays was discussed in Refs [32,33]. The QCD factorization [34,35] has been widely applied to studies of three-body charmless hadronic B meson decays [36][37][38][39][40][41][42][43][44][45][46][47][48], including, for instance, detailed investigation on factorization properties of the B + → π + π + π − mode in various regions of phase space [49]. The perturbative QCD (PQCD) approach based on the k T factorization theorem [50,51] has been employed in Refs. [52][53][54][55][56], where strong dynamics between two final-state hadrons in resonant regions are factorized into a new nonperturbative input, the two-hadron distribution amplitudes. An advantage of the PQCD factorization approach is that both nonresonant and resonant...

We extend our recent works on the P-wave twopion 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 P K π , which contains the final state interactions between the kaon and pion in the resonant region. The relativistic Breit-Wigner formula for the Pwave resonant state K * (892) is adopted to parameterize the time-like form factor F K π. We calculate the C P-averaged branching ratios and direct C P-violating asymmetries of the quasi-two-body decays B (s) → K * (892)h → K π h, with h = (π, K), in this work. It is shown that the agreement of theoretical results with the experimental data can be achieved, through which Gegenbauer moments of the Pwave kaon-pion distribution amplitudes are determined. The predictions in this work will be tested by the precise data from the LHCb and the future Belle II experiments.