We study Higgs boson production associated with single top or anti-top via t-channel weak boson exchange at the LHC. The process is an ideal probe of the top quark Yukawa coupling, because we can measure the relative phase of htt and hWW couplings, thanks to the significant interference between the two amplitudes. By choosing the emitted W momentum along the polar axis in the th (tbar h) rest frame, we obtain the helicity amplitudes for all the contributing subprocesses analytically, with possible CP phase of the Yukawa coupling. We study the azymuthal asymmetry between the W emission and the Wb(b) → t(tbar)h scattering planes, as well as several t and tbar polarization asymmetries as a signal of CP violating phase in the htt coupling. The azymuthal asymmetry of the top and anti-top events are found to be opposite in sign, while their polarizations perpendicular to the scattering plane are found to have the same sign with that of the CP phase. We identify the origin of the difference, and propose the possibility of direct CP violation test in pp collisions by comparing the top and anti-top polarization at the LHC.
