TauSpinner algorithms for including spin and New Physics effects in $\gamma \gamma \rightarrow \tau \tau$ process

The possible anomalous New Physics contributions to electric and magnetic dipole moments of the $\tau$ lepton has brought renewed interest in development of new charge-parity violating signatures in the $\tau$-pair production at Belle II energies, and also at higher energies of the LHC and the FCC. In this paper, we discuss effects of anomalous contributions to cross-section and spin correlations in the $\gamma\gamma \to \tau^-\tau^+$ production processes, with $\tau$ decays included. Such processes have been observed in the $pp$ and PbPb collisions at CERN LHC experiments. Because of complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular of event reweighting with studied New Physics phenomena. For the $\gamma\gamma$ processes, extensions of the Standard Model amplitudes are implemented in the TauSpinner program. This is mainly with electric and magnetic dipole moments in mind, but algorithm can be easily extended to other New Physics interactions, provided they can be encapsulated into similar form-factors in the Standard Model structure of matrix elements. Basic formulas and algorithm principles are presented, numerical examples are provided as illustration. Information on how to use the program is given in Appendix of the paper.