  Higgs boson pair production is traditionally considered to be of particular
interest for a measurement of the trilinear Higgs self-coupling. Yet it can
offer insights into other couplings as well, since - in an effective field
theory (EFT) parameterisation of potential new physics - both the production
cross section and kinematical properties of the Higgs boson pair depend on
various other Wilson coefficients of EFT operators. This note summarises the
ongoing efforts related to the development of EFT tools for Higgs boson pair
production in gluon fusion, and provides recommendations for the use of
distinct EFT parameterisations in the Higgs boson pair production process. This
document also outlines where further efforts are needed and provides a detailed
analysis of theoretical uncertainties. Additionally, benchmark scenarios are
updated. We also re-derive a parameterisation of the next-to-leading order
(NLO) QCD corrections in terms of the EFT Wilson coefficients both for the
total cross section and the distribution in the invariant mass of the Higgs
boson pair, providing for the first time also the covariance matrix. A
reweighting procedure making use of the newly derived coefficients is
validated, which can be used to significantly speed up experimental analyses.
