$CP$ violation from $\tau$, $t$ and $b$ dimension-6 Yukawa couplings --
  interplay of baryogenesis, EDM and Higgs physics
  We explore the implications of the Standard Model effective field theory
(SMEFT) with dimension-six terms involving the Higgs boson and third-generation
fermion fields on the rate of Higgs boson production and decay into fermions,
on the electric dipole moments (EDMs) of the electron, and on the baryon
asymmetry of the Universe. We study the consequences of allowing these
additional terms for each flavor separately and for combinations of two
flavors. We find that a complex $\tau$ Yukawa coupling can account for the
observed baryon asymmetry $Y_B^{\rm obs}$ within current LHC and EDM bounds. A
complex $b$ ($t$) Yukawa coupling can account for $4\%$ ($2\%$) of $Y_B^{\rm
obs}$, whereas a combination of the two can reach $12\%$. Combining $\tau$ with
either $t$ or $b$ enlarges the viable parameter space owing to cancellations in
the EDM and in either Higgs production times decay or the total Higgs width,
respectively. Interestingly, in such a scenario there exists a region in
parameter space where the SMEFT contributions to the electron EDM cancel and
collider signal strengths are precisely SM-like, while producing sufficient
baryon asymmetry. Measuring $CP$ violation in Higgs decays to $\tau$ leptons is
the smoking gun for this scenario.
