Polarization Effects in the Search for Dark Vector Boson at e⁺e⁻ Colliders^#

Abstract: We argue that the search for dark vector boson through (Formula presented.) can determine the Lorentz structure of (Formula presented.) couplings with the detection of leptonic decays (Formula presented.). We assume a general framework that the dark vector boson interacts with ordinary fermions through vector and axial-vector couplings. Taking (Formula presented.), we study the correlation between (Formula presented.) angle relative to (Formula presented.) beam direction in (Formula presented.) CM frame and (Formula presented.) angle relative to the boost direction of (Formula presented.) in (Formula presented.) rest frame. This correlation is useful for probing the Lorentz structure of (Formula presented.) couplings. We discuss the measurement of such correlation in Belle II detector.