  Various methods are used in the literature for predicting the lightest
CP-even Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM).
Fixed-order diagrammatic calculations capture all effects at a given order and
yield accurate results for scales of supersymmetric (SUSY) particles that are
not separated too much from the weak scale. Effective field theory calculations
allow a resummation of large logarithmic contributions up to all orders and
therefore yield accurate results for a high SUSY scale. A hybrid approach,
where both methods have been combined, is implemented in the computer code
FeynHiggs. So far, however, at large scales sizeable differences have been
observed between FeynHiggs and other pure EFT codes. In this work, the various
approaches are analytically compared with each other in a simple scenario in
which all SUSY mass scales are chosen to be equal to each other. Three main
sources are identified that account for the major part of the observed
differences. Firstly, it is shown that the scheme conversion of the input
parameters that is commonly used for the comparison of fixed-order results is
not adequate for the comparison of results containing a series of higher-order
logarithms. Secondly, the treatment of higher-order terms arising from the
determination of the Higgs propagator pole is addressed. Thirdly, the effect of
different parametrizations in particular of the top Yukawa coupling in the
non-logarithmic terms is investigated. Taking into account all of these
effects, in the considered simple scenario very good agreement is found for
scales above 1 TeV between the results obtained using the EFT approach and the
hybrid approach of FeynHiggs.
