Study of the K 1 ( 1270 ) - K 1 ( 1400 ) mixing in the decays B → J / Ψ K 1 ( 1270 ) , J / Ψ K 1 ( 1400 )

Abstract

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)+)=1.76-0.69+0.65×10-3,Br(B+→J/ΨK1(1400)+)=6.47-2.34+2.50×10-4, and Br(B0→J/ΨK1(1270)0)=(1.63-0.64+0.60)×10-3 with the mixing angle θK1=33∘, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that θK1∼33∘ is much more favored than 58∘. 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 θK1=33∘ and 58∘, 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.