Family Non-universal $Z^{\prime }$ Effects on $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ Decays in Perturbative QCD Approach

Abstract

The nonleptonic decays $B_{d,s}\to K^{\ast 0}{\overline{K}}^{\ast 0}$ are reanalyzed in perturbative QCD approach, which is based on the $k_{\mathrm{T}}$ factorization. In the standard model, the calculated branching fraction and longitudinal polarization fraction of $B_d\to K^{\ast 0}{\overline{K}}^{\ast 0}$ are in agreement with experimental measurements, while the predictions of $B_s\to K^{\ast 0}{\overline{K}}^{\ast 0}$ cannot agree with data simultaneously. The parameter that combines of longitudinal polarization fractions and branching fractions evaluated to be $L_{K^{\ast }{\overline{K}}^{\ast 0}}^{\mathrm{PQCD}}=12.7_{-3.2}^{+5.6}$, which is also larger than that abstracted from experimental measurements. We then study all observables by introducing a family non-universal $Z^{\prime }$ boson in $b\to sq\bar{q}$ transitions. In order to reduce the number of new parameters, we simplify the model as possible. It is found that with the fixed value ${\omega }_{B_s}=0.55$, these exists parameter space where all measurements, including the branching fraction, longitudinal polarization fraction and $L_{K^{\ast }{\overline{K}}^{\ast 0}}$-parameter, could be accommodated simultaneously. All our results and the small parameter space could be further tested in the running LHC experiments, Belle-II and future high-energy colliders.

Comments: 21 pages, 6 figures