Probing CP violation in $e^{+}e^{-}$ production of the Higgs boson and   toponia
  We study the CP violation in the Higgs boson and toponia production process at the ILC where the toponia are produced near the threshold. With the approximation that the production vertex of the Higgs boson and toponia is contact, and neglecting the P-wave toponia, we analytically calculated the density matrix for the production and decay of the toponia. Under these assumptions, the production spectrum of the toponia is solely determined by the spin quantum number, therefore the toponia can be either singlet or triplet. We find that the production rate of the singlet toponium is highly suppressed, and behaves just like the production of a P-wave toponia. In the case of the triplet toponium, three completely independent CP observables, namely azimuthal angles of lepton and anti-lepton in the toponium rest-frame as well as their sum, are predicted based on our analytical results, and checked by using the tree-level event generator. The non-trivial correlations come from the longitudinal-transverse interferences for the azimuthal angles of leptons, and the transverse-transverse interference for their sum. These three observables are well defined at the ILC, where the rest frame of the toponium can be reconstructed directly. Furthermore, the QCD-strong corrections, which are important near the threshold region, are also studied with the approximation of spin-independent QCD-Coulomb potential. While the total cross section is enhanced, the spin correlations predicted in this paper are not affected. 
Kaoru Hagiwara, Kai Ma, Hiroshi Yokoya
hep-ph hep-ex