https://doi.org/10.1140/epjc/s10052-022-10352-7
Regular Article - Theoretical Physics
Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays
in the perturbative QCD approach
School of Physical Science and Technology, Southwest University, 400715, Chongqing, China
Received:
17
September
2021
Accepted:
20
April
2022
Published online:
13
May
2022
Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays , which include the contributions of the intermediate resonances
,
,
,
, and
. The time-like form factors corresponding to the distribution amplitudes of the S-, P-, and D-wave of the kaon–pion pair were adopted in parameterized form, and describe the interactions between
and
in the resonance region. First, the decays
were calculated, followed by the calculation of the branching ratios of the decays
using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays
and
were obtained using the narrow-width approximation relation given by the Clebsch–Gordan coefficients. Our work shows that the
resonance is the main contributor to the total decay, and the branching ratio and the longitudinal polarization fraction of the
decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the
and
decay modes are very close, indicating that they can be regarded as the same meson state. Finally, the pQCD predictions for branching ratios of decays
are of the order of
and
, respectively, which can be verified using the ongoing LHCb and Belle II experiments.
© The Author(s) 2022
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