Polarization effects in the search for dark vector boson at $e^{+}{e}^{-}$ colliders

Abstract

We argue that the search for dark vector boson through $e^{+}{e}^{-}\to Z_d\gamma$ can determine the Lorentz structure of $Z_d{l}^{+}{l}^{-}$ couplings with the detection of leptonic decays $Z_d\to l^{+}{l}^{-}$. 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, $Z_d$ is transversely polarized in the limit $m_{Z_d}\ll \sqrt{s}$. On the other hand, the fraction of longitudinal $Z_d$ is non-negligible for $m_{Z_d}$ comparable to $\sqrt{s}$. Such polarization effects can be analyzed through angular distributions of final-state particles in $Z_d$ decays. Taking $l^{\pm }\equiv {\mu }^{\pm }$, we study the correlation between $Z_d$ angle relative to $e^{-}$ beam direction in $e^{+}{e}^{-}$ CM frame and ${\mu }^{-}$ angle relative to the boost direction of $Z_d$ in $Z_d$ rest frame. This correlation is shown to be useful for probing the Lorentz structure of $Z_d{l}^{+}{l}^{-}$ couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.

arXiv commentTable revised and figures added in Sec. IV; accepted for publication in Phys. Rev. D

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