Polarization effects in the search for a dark vector boson at e+e- colliders

We argue that the search for dark vector boson through e+e-→Zdγ can determine the Lorentz structure of Zdl+l- couplings with the detection of leptonic decays Zd→l+l-. We assume a general framework that the dark vector boson interacts with ordinary fermions through vector and axial-vector couplings. As a consequence of Ward-Takahashi identity, Zd is transversely polarized in the limit mZd s. On the other hand, the fraction of longitudinal Zd is non-negligible for mZd comparable to s. Such polarization effects can be analyzed through angular distributions of final-state particles in Zd decays. Taking l±μ±, we study the correlation between Zd angle relative to e- beam direction in e+e- center of momentum frame and μ- angle relative to the boost direction of Zd in Zd rest frame. This correlation is shown to be useful for probing the Lorentz structure of Zdl+l- couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.