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

Abstract

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

12 pages, 10 figures, 2 tables, Version accepted for publication in EPJC