Deep Neural Network application: Higgs boson CP state mixing angle in H to tau tau decay and at LHC

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.