  In a supersymmetric theory, large mass hierarchies can lead to large
uncertainties in fixed-order calculations of the Standard Model (SM)-like Higgs
mass. A reliable prediction is then obtained by performing the calculation in
an effective field theory (EFT) framework, involving a matching to the full
supersymmetric theory at the high scale to include contributions from the heavy
particles, and a subsequent renormalisation-group running down to the low
scale. We report on the prediction of the SM-like Higgs mass within the
CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM) in a
scenario where all non-SM particles feature TeV-scale masses. The matching
conditions are calculated at full one-loop order using two approaches. These
are the matching of the quartic Higgs couplings as well as of the SM-like Higgs
pole masses of the low- and high-scale theory. A comparison between the two
methods allows us to estimate the size of terms suppressed by the heavy mass
scale that are neglected in a pure EFT calculation as given by the
quartic-coupling matching. Furthermore, we study the different sources of
uncertainty which enter our calculation as well as the effect of CP-violating
phases on the Higgs mass prediction. The matching calculation is implemented in
a new version of the public program package NMSSMCALC.
