The -wave resonance contributions to the three-body decays in perturbative QCD approach
In this paper, we study the three-body decays by employing the perturbative QCD (PQCD) factorization approach. We evaluate the -wave resonance contributions by using the two-pion distribution amplitude . The Breit-Wigner formula for the , , and resonances and the Flatté model for the resonance are adopted to parameterize the time-like scalar form factors . We also use the D.~V.~Bugg model to parameterize the and compare the relevant theoretical predictions from different models. We found the following results: (a) the PQCD predictions for the branching ratios are for Breit-Wigner model and for D.~V.~Bugg model; (b) when the contributions from are all taken into account; and (c) The considered decays could be measured at the ongoing LHCb exp