Study of the $$K_1(1270)-K_1(1400)$$ K1(1270)-K1(1400) mixing in the decays $$B\rightarrow J/\Psi K_1(1270), J/\Psi K_1(1400)$$ B→J/ΨK1(1270),J/ΨK1(1400) - Zhi-Qing Zhang (European Physical Journal C: Particles and Fields, 2018)
Abstract We study the B meson decays $$B\rightarrow J/\Psi K_1(1270,1400)$$ 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 $$Br(B^+\rightarrow J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times 10^{-3}, Br(B^+\rightarrow J/\Psi K_1(1400)^+)=6.47^{+2.50}_{-2.34}\times 10^{-4}$$ 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 $$Br(B^0\rightarrow J/\Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times 10^{-3}$$ Br(B0→J/ΨK1(1270)0)=(1.63-0.64+0.60)×10-3 with the mixing angle $$\theta _{K_1}=33^\circ $$ θK1=33∘ , which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $$\theta _{K_1}\sim 33^\circ $$ θK1∼33∘ is much more favored than $$58^{\circ }$$ 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 $$\theta _{K_1}=33^\circ $$ θK1=33∘ and $$58^\circ $$ 58∘ , respectively. The direct CP violations of the two charged decays $$B^+\rightarrow J/\Psi K_1(1270,1400)^+$$ B+→J/ΨK1(1270,1400)+ are very small $$(10^{-4}\sim 10^{-5})$$ (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 $$J/\Psi $$ J/Ψ meson. These results can be tested at the running LHCb and forthcoming Super-B experiments.