https://doi.org/10.1140/epjc/s10052-017-5193-y
Regular Article - Theoretical Physics
Branching ratios, CP asymmetries and polarizations of 
decays
1
College of Sciences, North China University of Science and Technology, Tangshan, 063009, China
2
Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China
* e-mail: jindui1127@126.com
Received:
15
July
2017
Accepted:
2
September
2017
Published online:
14
September
2017
We analyze the non-leptonic decays 
with 
by employing the perturbative QCD (pQCD) factorization approach. Here the branching ratios, the CP asymmetries and the complete set of polarization observables are investigated systematically. Besides the traditional contributions from the factorizable and non-factorizable diagrams at the leading order, the next-to-leading order (NLO) vertex corrections could also provide considerable contributions. The pQCD predictions for the branching ratios of the 
decays are consistent with the measured values within errors. As for 
decays, the branching ratios can reach the order of 
and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct CP asymmetries of the considered decays are very small. Thus the observation of any large direct CP asymmetry for these decays will be a signal for new physics. The mixing-induced CP asymmetries in the neutral modes are very close to 
, which suggests that these channels can give a cross-check on the measurement of the Cabbibo–Kobayashi–Maskawa (CKM) angle 
and 
. We find that the longitudinal polarization fractions 
are suppressed to 
due to the large non-factorizable contributions. The magnitudes and phases of the two transverse amplitudes 
and 
are roughly equal, which is an indication for the approximate light-quark helicity conservation in these decays. The overall polarization observables of 
and 
channels are also in good agreement with the experimental measurements as reported by LHCb and BaBar. Other results can also be tested by the LHCb and Belle-II experiments.
© The Author(s), 2017
