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The consecutive steps of cascade decay initiated by H to tau tau can be useful for the measurement of Higgs couplings and in particular of the Higgs boson parity. In the previous papers we have found, that multi-dimensional signatures of the tau^pm to pi^pm pi^0 nu and tau^pm to 3pi^pm nu decays can be used to distinguish between scalar and pseudoscalar Higgs state. The Machine Learning techniques (ML) of binary classification, offered break-through opportunities to manage such complex multidimensional signatures. The classification between two possible CP states: scalar and pseudoscalar, is now extended to the measurement of the hypothetical mixing angle of Higgs boson parity states. The functional dependence of H to tau tau matrix element on the mixing angle is predicted by theory. The potential to determine preferred mixing angle of the Higgs boson events sample including $\tau$-decays is studied using Deep Neural Network. The problem is adressed as classification or regression with the aim to determine the per-event: a) probability distribution (spin weight) of the mixing angle; b) parameters of the functional form of the spin weight; c) the most preferred mixing angle. Performance of methods are evaluated and compared. Numerical results are collected., Comment: 20 pages 21 figures

Machine Learning (ML) techniques are rapidly finding a place among the methods of High Energy Physics data analysis. Different approaches are explored concerning how much effort should be put into building high-level variables based on physics insight into the problem, and when it is enough to rely on low-level ones, allowing ML methods to find patterns without explicit physics model. In this paper we continue the discussion of previous publications on the CP state of the Higgs boson measurement of the H to tau tau decay channel with the consecutive tau^pm to rho^pm nu; rho^pm to pi^pm pi^0 and tau^pm to a_1^pm nu; a_1^pm to rho^0 pi^pm to 3 pi^pm cascade decays. The discrimination of the Higgs boson CP state is studied as a binary classification problem between CP-even (scalar) and CP-odd (pseudoscalar), using Deep Neural Network (DNN). Improvements on the classification from the constraints on directly non-measurable outgoing neutrinos are discussed. We find, that once added, they enhance the sensitivity sizably, even if only imperfect information is provided. In addition to DNN we also evaluate and compare other ML methods: Boosted Trees (BT), Random Forest (RF) and Support Vector Machine (SVN)., Comment: 1+20 pages, 9 figures, 6 tables, extended content and improved readability