Abstract
We argue that the search for dark vector boson through $e^+e^-\to Z_d\gamma$ can determine the Lorentz structure of $Z_dl^+l^-$ 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 $Z_dl^+l^-$ couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.
Highlights
Searching for dark matter (DM) is one of the major endeavors in the present day particle physics community
We argue that the search for dark vector boson through eþe− → Zdγ can determine the Lorentz structure of Zdlþl− couplings with the detection of leptonic decays Zd → lþl−
Taking lÆ ≡ μÆ, we study the correlation between Zd angle relative to e− beam direction in eþe− center of momentum frame and μ− angle relative to the boost direction of Zd in Zd rest frame
Summary
Searching for dark matter (DM) is one of the major endeavors in the present day particle physics community. The visible mode requires a full reconstruction of Zd peak through measuring the energy and momentum of lepton or light hadron pairs from Zd decays [23,24,25,26,27,28], while the invisible mode looks for the peak of missing mass at mZd given by M2mass 1⁄4 ðPe− þ Peþ − PγÞ2 [29] We note that both phenomenological and experimental studies mentioned above consider only the dark photon scenario, i.e., Zd interacts with SM fermions only via electromagnetic current. We focus on the prospect of detecting Zd and measuring the parity violation parameter in its interaction with SM fermions with eþe− → Zdγ followed by Zd → μþμ− decay at Belle II.
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