LAUSR

The consecutive steps of cascade decay initiated by $H\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\tau}$ 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 multidimensional signatures of the ${\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$ and ${\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\nu}$ 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 $H\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\tau}$ matrix element on the mixing angle is predicted by theory. The potential to determine preferred mixing angle of the Higgs boson events sample including $\ensuremath{\tau}$-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.