The possible anomalous New Physics contributions to dipole and weak dipole moments of the \ (\) lepton bring renewed interest in development and revisiting charge-parity violating signatures in \ (\) -pair production in \ (Z\) -boson decay at energies of the LHC. In this paper, we discuss effects of anomalous contributions to polarisation and spin correlations in the \ (q q ^+ ^-\) production processes, with \ (\) decays included. Due to the complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular for event reweighing with studied New Physics phenomena. Extensions of the Standard Model spin amplitudes, within the Improved Born Approximation used for the matrix element, are implemented in the TauSpinner program. This is mainly with \ (\) dipole and weak dipole moments in mind, but is applicable to arbitrary New Physics interactions, provided they can be encapsulated into the Standard Model \ (2 2\) structure of matrix element extensions. The implementation allows one also to introduce an arbitrary phase-shift between vector and axial-vector couplings of \ (Z\) boson to \ (\) leptons, which would have impact on the observed transverse spin correlations. Basic formulas and algorithm principles are presented, together with distributions for the spin-correlation matrix. Numerical examples of impact on experimental signatures are shown in the case of \ (^ ^ _ ^ ⁰ _ \) decays. Information on how to use and configure the TauSpinner program is given in Appendix B. Abstract Published by the Jagiellonian University 2026 authors
Korchin et al. (Mon,) studied this question.