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Spin and Chirality Effects in Antler-Topology Processes at High Energy $e^+e^-$ Colliders

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes $e^+e^-\to\mathcal{P}^+\mathcal{P}^-\to (\ell^+ \mathcal{D}^0) (\ell^-\mathcal{\bar{D}}^0)$ at high energy $e^+e^-$ colliders with polarized beams. Generally the production process $e^+e^-\to\mathcal{P}^+\mathcal{P}^-$ can occur not only through the $s$-channel exchange of vector bosons, $\mathcal{V}^0$, including the neutral Standard Model (SM) gauge bosons, $γ$ and $Z$, but also through the $s$- and $t$-channel exchanges of new neutral states, $\mathcal{S}^0$ and $\mathcal{T}^0$, and the $u$-channel exchange of new doubly-charged states, $\mathcal{U}^{--}$. The general set of (non-chiral) three-point couplings of the new particles and leptons allowed in a renormalizable quantum field theory is considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for $\mathcal{P}^+\mathcal{P}^-$ pair production in $e^+e^-$ collisions with longitudinal and transverse polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high energy $e^+e^-$ collider.