Within the perturbative QCD approach, we recalculate the branching ratio and polarization fractions of the pure annihilation decay $B\to \varphi \varphi$ in both the standard model and the family nonuniversal $Z^{\prime }$ model. We find that this decay is dominated by the longitudinal part, while the transverse parts are negligibly due to the absence of the $(S-P)(S+P)$-type operator. In the standard model, the branching ratio is predicted as $({4.4}_{-0.6-0.5}^{+0.8+0.3})\times {10}^{-8}$, which is larger than the previous predictions. With an additional $Z^{\prime }$ boson, the branching ratio can be enhanced by a factor of 2 or reduced one-half in the allowed parameter space. These results will be tested by the ongoing LHCb experiment and forthcoming Super-$B$ experiments.

• Received 2 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.014003