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We study the prospects of measuring the CP property of the Higgs ($h$)coupling to tau leptons using the vector boson fusion (VBF) production mode atthe high-luminosity LHC. Utilizing the previously proposed angle between theplanes spanned by the momentum vectors of the $(\pi^+\pi^0)$ and $(\pi^-\pi^0)$ pairs originating in $\tau^\pm$ decays as the CP-odd observable, weperform a detailed Monte Carlo analysis, taking into account the relevantstandard model backgrounds, as well as detector resolution effects. We findthat excluding a pure CP-odd coupling hypothesis requires $\mathcal{O}(400{~\rm fb}^{-1})$ luminosity at the 14 TeV LHC, and values of the CP-mixingangle larger than about $25^\circ$ can be excluded at $95\%$ confidence levelusing $3 {~\rm ab}^{-1}$ data. It is observed that the uncertainty in theangular resolution of the neutral pion momenta does not constitute asignificant hurdle. Achieving a signal to background ratio ($S/B$) close toone, while keeping a high enough signal yield required to study the angulardistributions selects out VBF as a promising mode to probe the CP nature of the$h\tau\tau$ coupling, with gluon fusion suffering from a low $S/B$, and the$W^\pm h/Zh$ mode (with leptonically decaying $W^\pm /Z$) having a much smallersignal rate.

Measuring the CP property of Higgs coupling to tau leptons in the VBF channel at the LHC