  In this paper, we present the computation of the Higgs boson pair production
cross section, both inclusive as well as differential on the invariant mass
distribution, at next-to-next-to-leading order (NNLO) in QCD including effects
of new physics beyond the standard model. We parametrize the effects of new
physics with the relevant dimension 6 operators in a standard model effective
field theory (EFT) approach and examine their phenomenology. The dependence of
the NNLO $K$-factor on the EFT couplings is analysed, finding that, while
rather flat for a number of EFT coefficients, it can considerably differ from
the standard model value in some particular regions of the parameter space. We
present explicit examples of (almost) degeneracy in the NNLO cross-section with
respect to the anomalous couplings, showing that the invariant mass
distribution has a much larger sensitivity to phenomena beyond the standard
model and can be used as a tool to discriminate their effect.
