Unraveling the CP phase of top-Higgs coupling in associated production at the LHC

We study the sensitivity of top polarization observables to the CP phase $\zeta_t$ in the top Yukawa coupling in the process $pp\to thj$ at the 14 TeV high-luminosity run of the Large Hadron Collider (HL-LHC). We calculate the top polarization in this process as well as an azimuthal asymmetry of the charged lepton arising from the decay of the top in the lab frame. We find that the dependence of this lab-frame azimuthal asymmetry on the phase $\zeta_t$ closely resembles the dependence of the top polarization on $\zeta_t$. As compared to the cross section, which is sensitive to $\zeta_t$ for larger values, the lepton azimuthal asymmetry can provide a sensitive measurement of $\zeta_t$ for smaller values.