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→ττ 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 multidimensional signatures of the τ±→π±π0ν and τ±→3π±ν 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→ττ matrix element on the mixing angle is predicted by theory. The potential to determine preferred mixing angle of the Higgs boson events sample including τ-decays is studied using deep neural network. The problem is addressed 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 proposed methods is evaluated and compared.