Spin and chirality effects in antler-topology processes at high energy \varvec{e^+e^-} colliders

We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes \(e^+e^-\rightarrow \mathcal {P}^+\mathcal {P}^-\rightarrow (\ell ^+ \mathcal {D}^0) (\ell ^-\mathcal {\bar{D}}^0)\) at high-energy \(e^+e^-\) colliders with polarized beams. Generally the production process \(e^+e^-\rightarrow \mathcal {P}^+\mathcal {P}^-\) can occur not only through the s-channel exchange of vector bosons, \(\mathcal {V}^0\), including the neutral Standard Model (SM) gauge bosons, \(\gamma \) 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.