Study of the $K_1(1270)-K_1(1400)$ mixing in the decays $B\to J/\Psi K_1(1270),J/\Psi K_1(1400)$

Abstract

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 $Br(B^{+}\to J/\Psi K_1(1270{)}^{+})=1.76_{-0.69}^{+0.65}\times 10^{-3},Br(B^{+}\to J/\Psi K_1(1400{)}^{+})=7.03_{-2.52}^{+2.70}\times 10^{-4}$, and $Br(B^0\to J/\Psi K_1(1270{)}^0)=(1.63_{-0.64}^{+0.60})\times 10^{-3}$ 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 ${\theta }_{K_1}\sim 33^{\circ }$ 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 $(10^{-4}\sim 10^{-5})$, 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.

arXiv comment14 pages,3 figures,to appear in EPJC

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