Measuring CP nature of $$h\tau {{\bar{\tau }}}$$ coupling at $$e^-p$$ collider

Abstract The proposed future $$e^- p$$ e - p collider provides sufficient energies to produce the Standard Model Higgs Boson ( h ) through $$W^\pm $$ W ± and Z -Boson fusion in charged neutral current modes, respectively measure its properties. We take this opportunity investigate prospect of measuring CP properties $$h \rightarrow \tau ^{+} ^{-}$$ h → τ + , where $$\tau ^{-}\,\left( ^{+}\right) decays a pion $$\pi ^-\,\left( \pi ^+\right) π ^0$$ 0 association with neutrino (anti-neutrino). An interesting sensitive angular observable $$\alpha _{\mathrm{CP}}$$ α CP between two -leptons decay plane ^+\pi ^-$$ centre mass frame is investigated work. For fixed electron energy 150 GeV along 7 (50) TeV proton energy, phase can be measured approximately $$25^\circ 25 ∘ $$14^\circ 14 at integrated luminosity 1 ab $$^{-1}$$ 1 for −80% polarised 95% confidence level.