Studying the $B^0\to J/\psi h_1$ decays with $h_1(1170)-h_1(1415)$ mixing in the perturbative QCD approach

Abstract

In this paper, we study the $B^0\to J/\psi h_1$ decays for the first time by using perturbative QCD approach up to the presently known next-to-leading order accuracy. The vertex corrections present significant contribution to the amplitude. In the calculation, the mixing between two light axial-vector mesons $h_1(1170)$ and $h_1(1415)$ are also studied in detail. The observables including the branching ratios, polarization fractions and $CP$ asymmetries are predicted and discussed explicitly. It is found that the $B^0\to J/\psi h_1$ decays have relatively large branching fractions, which are generally at the order of $\mathcal{O}(10^{-6}\sim 10^{-3})$, and thus are possible to be observed by the LHCb and Belle-II experiments in the near future. Moreover, they are very sensitive to the mixing angle $\theta$ and can be used to test the values of $\theta$. In addition, some ratios between the branching fractions of $B^0\to J/\psi h_1$ decays can provide much stronger constraints on $\theta$ due to their relatively small theoretical errors. The $B^0\to J/\psi h_1$ decays are generally dominated by the longitudinal polarization contributions, specifically, $f_L(B^0\to J/\psi h_1)>80\%$, except for the case that $\theta \sim 35^{\circ }$ and $-55^{\circ }$. Unfortunately, the direct $CP$ asymmetries of $B^0\to J/\psi h_1$ decays are too small to be observed soon even if the effect of $\theta$ is considered. The future precise measurements on $B^0\to J/\psi h_1$ decays are expected for testing these theoretical findings and exploring the interesting nature of $h_1(1170)$ and $h_1(1415)$.

Comments: 23 pages, 6 figures, 8 tables