  Higgs pair production through gluon fusion is an important process at the LHC
to test the dynamics underlying electroweak symmetry breaking. Higgs sectors
beyond the Standard Model (SM) can substantially modify this cross section
through novel couplings not present in the SM or the on-shell production of new
heavy Higgs bosons that subsequently decay into Higgs pairs. CP violation in
the Higgs sector is important for the explanation of the observed
matter-antimatter asymmetry through electroweak baryogenesis. In this work we
compute the next-to-leading order (NLO) QCD corrections in the heavy top quark
limit, including the effects of CP violation in the Higgs sector. We choose the
effective theory (EFT) approach, which provides a rather model-independent way
to explore New Physics (NP) effects by adding dimension-6 operators, both
CP-conserving and CP-violating ones, to the SM Lagrangian. Furthermore, we
perform the computation within a specific UV-complete model and choose as
benchmark model the general 2-Higgs-Doublet Model with CP violation, the C2HDM.
Depending on the dimension-6 coefficients, the relative NLO QCD corrections are
affected by several per cent through the new CP-violating operators. This is
also the case for SM-like Higgs pair production in the C2HDM, while the
relative QCD corrections in the production of heavier C2HDM Higgs boson pairs
deviate more strongly from the SM case. The absolute cross sections both in the
EFT and the C2HDM can be modified by more than an order of magnitude. In
particular, in the C2HDM the resonant production of Higgs pairs can by far
exceed the SM cross section.
