Potential for optimizing Higgs boson CP measurement in H to tau tau decay at LHC and ML techniques

We investigate potential for measuring CP state of the Higgs boson in the H to tau tau$ decay with consecutive tau-lepton decays in channels: tau^+- to rho^+- nu_tau and tau^+- to a1^+- nu_tau combined. Subsequent decays rho^+- to pi^+- pi^0, a1^+- to rho^0 pi^+- and rho^0 to pi^+ pi^- are taken into account. We will explore extensions of the method, where acoplanarity angle for the planes build on the visible decay products, pi^+- pi^0 of tau^+- to pi^pm pi^0 nu_tau, was used. The angle is sensitive to transverse spin correlations, thus to parity. We show, that in the case of the cascade decays of tau to a1 nu, information on the CP state of Higgs can be extracted from the acoplanarity angles as well. Because in the cascade decay a1^+- to rho^0 pi^pm,rho^0 to pi^+ pi^- up to four planes can be defined, up to 16 distinct acoplanarity angles are available for H \to tau tau to a1^+ a1^- nu nu decays. These acoplanarities carry in part supplementary but also correlated information. It is thus cumbersome to evaluate an overall sensitivity. We investigate sensitivity potential of such analysis, by developing and implementing model in the Machine Learning (ML) techniques. We quantify possible improvements when multi-dimensional phase-space of outgoing decay products directions is used, instead of 1-dimensional projections i.e. the acoplanarity angles. We do not take into account ambiguities resulting from detector uncertainties or background contamination, we concentrate on usefulness of ML methods and tau to 3pi nu decays for Higgs boson parity measurement.