Does the top-Higgs coupling contain a CP-violating component?
In plain words
The SM predicts that the interaction between the Higgs and the top quark respects CP, the combined mirror and particle-antiparticle symmetry. A CP-violating part would be a new source of the matter-antimatter difference.
Precise statement
With L ~ -(y_t/sqrt 2) kappa_t h tbar (cos alpha + i gamma_5 sin alpha) t, the SM has $\alpha = 0$. ATLAS ttH and tH with $H \to \gamma \gamma$ excludes $\mid\alpha\mid > 43\ \mathrm{deg}$ at 95 percent CL (Phys. Rev. Lett. 125, 061802, 2020). An answer is alpha determined to a few degrees, or a bound which, combined with electron EDM limits, decides whether top-Higgs CP violation can supply electroweak baryogenesis.
What would settle it
HL-LHC angular analyses of ttH and tH production in several Higgs decay channels, combined with EDM limits on the loop-induced CP-odd operators.
Status in the literature
LHC Run 2 data agree with $\alpha = 0$ and exclude a purely CP-odd top Yukawa coupling.