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

TL;DR

This paper investigates the effects of a family non-universal $Z'$ boson on $B_{d,s} o K^{*0} ar{K}^{*0}$ decays within the perturbative QCD framework, aiming to reconcile theoretical predictions with experimental data.

Contribution

It introduces a simplified family non-universal $Z'$ model to explain discrepancies in $B_{d,s} o K^{*0} ar{K}^{*0}$ decay observables, aligning theory with experiments.

Findings

Standard model predictions agree with $B_d$ decays but not $B_s$ decays.

Inclusion of $Z'$ boson allows simultaneous fit to multiple observables.

Parameter space identified for $Z'$ effects consistent with current measurements.

Abstract

The nonleptonic decays $B_{d,s} \to K^{*0} {\overline K^{*0}}$ are reanalyzed in perturbative QCD approach, which is based on the $k_{\rm T}$ factorization. In the standard model, the calculated branching fraction and longitudinal polarization fraction of $B_{d} \to K^{*0} {\overline K^{*0}}$ are in agreement with experimental measurements, while the predictions of $B_{s} \to K^{*0} {\overline K^{*0}}$ cannot agree with data simultaneously. The parameter that combines of longitudinal polarization fractions and branching fractions evaluated to be $L_{K^*\overline{K}^{*0}}^{\rm PQCD}= 12.7^{+5.6} _{-3.2}$, 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 $b\to s q\bar q$ 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 $L_{K^*\overline{K}^{*0}}$-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.