Study of the K₁(1270) - K₁(1400) mixing in the decays B → J/ΨK₁(1270), J/ΨK₁(1400)

We study the B meson decays B → J/ΨK₁(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 predicted as Br(B⁺ → J/ΨK₁(1270)⁺) = 1.76^+0.65_-0.69 x 10^-3, Br(B⁺ → J/ΨK₁(1400)⁺) = 6.47^+2.50_-2.34 x 10^-4, and Br(B⁰ → J/ΨK₁(1270)⁰) = (1.63^+0.60_-0.64) x 10^-3 with the mixing angle θ_K1 = 33 ^circle, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that θ_K1 ∝ 33 ^circle is much more favored than 58 ^circle. 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 θ_K1 = 33 ^circle and 58 ^circle, respectively. The direct CP violations of the two charged decays B⁺ → J/ΨK₁(1270, 1400)⁺ are very small (10^-4 ∝ 10^-5) 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 J/Ψ meson. These results can be tested at the running LHCb and forthcoming Super-B experiments. (orig.)