We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ 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 $Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{ +0.65}_{ -0.69}\times10^{ -3}, Br(B^+\to J/\Psi K_1(1400)^+)=7.03^{ +2.70}_{ -2.52}\times10^{ -4}$, and $Br(B^0\to J/\Psi K_1(1270)^0)=(1.63^{ +0.60}_{ -0.64})\times10^{ -3}$ with the mixing angle $\theta_{ K_1}=33^\circ$, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $\theta_{ K_1}\sim33^\circ$ is much more favored than $58^{ \circ}$. Furthermore, we also give the predictions for the polarization fractions, direct CP violations from the different polarization components, the relative phase angles for the considered decays with the mixing angle $\theta_{ K_1}=33^\circ$ and $58^\circ$, respectively. The direct CP violations of the two charged decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{ -4}\sim10^{ -5})$, because there is no weak phase until up to $\mathcal{ O}(\lambda^4)$ with the Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the running LHCb and forthcoming Super-B experiments.
Categories: hep-ph