LHC Higgs CP Sensitive Observables in H to tau^+ tau^-; tau^pm to (3pi)^pm nu and Machine Learning Benefits

In phenomenological preparation for new measurements one searches for the carriers of quality signatures. Often, the first approach quantities may be difficult to measure or to provide sufficiently precise predictions for comparisons. Complexity of necessary details grow with precision. To achieve the goal one can not break the theory principles, and take into account effects which could be ignored earlier. Mixed approach where dominant effects are taken into account with intuitive even simplistic approach was developed. Non dominant corrections were controlled with the help of Monte Carlo simulations. Concept of Optimal Variables was successfully applied for many measurements. New techniques, like Machine Learning, offer solutions to exploit multidimensional signatures. Complementarity of these new and old approaches is studied for the example of Higgs Boson CP-parity measurements in H to tau^+tau^-, tau^pm to nu (3pi)^pm cascade decays.