  We study the alignment of Yukawa couplings in the framework of general two
Higgs doublet models (2HDMs) considering a scenario in which the lightest
neutral Higgs boson is purely CP even while the two heavier neutral Higgs
bosons are allowed to mix in the presence of nontrivial CP-violating phases in
the Higgs potential. Identifying the lightest neutral Higgs boson as the 125
GeV one discovered at the LHC, we find that the alignment of Yukawa couplings
without decoupling could be easily achieved in the type-I 2HDM with no much
conflict with the current LHC Higgs precision data. Otherwise, we observe that
the Yukawa couplings of the lightest Higgs boson could decouple much slowly
compared to the Higgs coupling to a pair of massive vector bosons and they
significantly deviate from the corresponding SM values even when the deviation
of the Higgs to vector boson coupling is below the percent level. On the other
hand, independently of 2HDM type and regardless of decoupling, we find a
wrong-sign alignment limit of the Yukawa couplings in which the Yukawa
couplings to the down-type quarks and/or those to the charged leptons are equal
in strength but opposite in sign to the corresponding SM ones. The magnitude
and sign of the up-type quark Yukawa couplings remain the same as in the SM.
Accordingly, in this limit, all four types of 2HDMs are viable against the LHC
Higgs precision data.
