https://doi.org/10.1140/epjc/s10052-018-5674-7
Regular Article - Theoretical Physics
Study of the 
mixing in the decays 
1
Department of Physics, Henan University of Technology, Zhengzhou, 450052, Henan, People’s Republic of China
2
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China
* e-mail: guohongxia@zzu.edu.cn
Received:
29
May
2017
Accepted:
25
February
2018
Published online:
15
March
2018
We study the B meson decays 
in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are predicted as 
, and 
with the mixing angle 
, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that 
is much more favored than 
. Furthermore, we also give the predictions of the polarization fractions, the direct CP violations, the relative phase angles for the considered decays with the mixing angle and 
, respectively. The direct CP violations of the two charged decays 
are very small 
, because the weak phase is very tiny. In order to check the dependence of the results on the nonperturbative input parameters, we also calculate them by using the harmonic-oscillator type wave functions for the 
meson. These results can be tested at the running LHCb and forthcoming Super-B experiments.
© The Author(s), 2018
