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The search for a new source of CP violation is one of the most importantendeavors in particle physics. A particularly interesting way to perform thissearch is to probe the CP phase in the $h\tau\tau$ coupling, as the phase iscurrently completely unconstrained by all existing data. Recently, a novelvariable $\Theta$ was proposed for measuring the CP phase in the $h\tau\tau$coupling through the $\tau^\pm \to \pi^\pm \pi^0 \nu$ decay mode. We examinetwo crucial questions that the real LHC detectors must face, namely, the issueof neutrino reconstruction and the effects of finite detector resolution. Forthe former, we find strong evidence that the collinear approximation is thebest for the $\Theta$ variable. For the latter, we find that the angularresolution is actually not an issue even though the reconstruction of $\Theta$requires resolving the highly collimated $\pi^\pm$'s and $\pi^0$'s from the$\tau$ decays. Instead, we find that it is the missing transverse energyresolution that significantly limits the LHC reach for measuring the CP phasevia $\Theta$. With the current missing energy resolution, we find that with$\sim 1000\,\textrm{fb}^{-1}$ the CP phase hypotheses $\Delta = 0^\circ$ (thestandard model value) and $\Delta = 90^\circ$ can be distinguished, at most, atthe 95\% confidence level.

Prospect for measuring the CP phase in the $h\tau\tau$ coupling at the LHC