Determining the relative size of the CP-even and CP-odd Higgs Boson Couplings to a Fermion at the LHC

We demonstrate that the relative size of the CP-even and CP-odd couplings of a Higgs boson to $t\anti t$ can be determined at the LHC at a level that is very useful in discriminating between models, provided that a Higgs signal can be observed at a reasonable $S/\sqrt B$ level in the $t\anti t\h$ (with $\h\to\gamma\gamma$ or $b\anti b)$ channels. In particular, the CP-even nature of a SM-like Higgs boson's coupling to $t\anti t$ can be confirmed with very substantial statistical significance using the $t\anti t \h$ ($\h\to \gamma\gamma$) production/decay mode. The key to achieving good discrimination between models is to make full use of the difference in the final state distributions for different ratios of the CP-even to CP-odd couplings. For our analysis, we employ the very convenient and simple optimal analysis procedures derived previously.