Quasi-two-body decays B → ηc(1S, 2S) [ρ(770), ρ(1450), ρ(1700) →] ππ in the perturbative QCD approach

In this paper, we calculated the branching ratios of the quasi-two-body decays B -> eta(c)(1S, 2S) [rho(770), rho(1450), rho(1700) ->]pi pi by employing the perturbative QCD (PQCD) approach. The contributions from the P-wave resonances rho(770), rho(1450) and rho(1700) were taken into account. The two-pion distribution amplitude Phi(P)(pi pi) is parameterized by the vector current time-like form factor F-pi, to study the considered decay modes. We found that (a) the PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the order of 10(-7) similar to 10(-6), while the two-body decay rates B(B -> eta(c)(1S, 2S) (rho(1450), rho(1700))) are extracted from those for the corresponding quasi-two-body decays; (b) the whole pattern of the pion form factor-squared |F-pi|(2) measured by the BABAR Collaboration could be understood based on our theoretical results; (c) the general expectation based on the similarity between B -> eta(c)pi pi and B -> J/Psi pi pi decays are confirmed: R-2(eta(c)) approximate to 0.45 is consistent with the measured R-2 (J/Psi) approximate to 0.56 +/- 0.09 within errors; and (d) new ratios R-3 (eta(c) (1S)) and R-4 (eta(c) (2S)) among the branching ratios of the considered decay modes are defined and could be tested by future experiments. (C) 2017 The Authors. Published by Elsevier B.V.