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The search and the probe of the fundamental properties of Higgs boson(s) and, in particular, the determination of their charge conjugation and parity (CP) quantum numbers, is one of the main tasks of future high-energy colliders.
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The heavy quark polarization in e + e − → t t ¯ Φ e^{+}e^{-}\rightarrow t\bar{t}\Phi has also been calculated in a 2HDM in C.S. Huang and S.H. Zhu, Phys. Rev. D65 (2002) 077702, but not interpreted
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Central diffractive exclusive Higgs production at the LHC would have also been useful to probe CP but the rates for a SM–like Higgs boson are unfortunately too low; see e.g., A. Kaidalov et al
See for instance: S.Y. Choi et al
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The additional diagram in a 2HDM where the t t ¯ t\bar{t} pair originates from the splitting of a CP–even (odd) scalar particle for (pseudo)scalar Higgs production, contributes very little unless Φ → t t ¯ \Phi\to t\bar{t} decays are allowed
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R.M. Godbole, S.D. Rindani and R.K. Singh, JHEP 12 (2006) 021
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