Polarization effects in the search for dark vector boson at \(e^+e^-\) colliders

• Published in: arXiv.org
• Main Authors: Fei-Fan, Lee, Guey-Lin, Lin, Vo, Quang Nhat
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 28.12.2020
• Subjects: Correlation analysis; Couplings; Energy resolution; Fermions; Particle decay; Polarization
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2008.07769

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.