PYTHIA already simulates a Two Higgs Doublet Model (2HDM) obeying tree-level
relations fixed by two parameters, which can be conveniently taken as the
ratio of doublet vacuum expectation values , and the
pseudoscalar mass
(as noted earlier, for the non-SUSY
implementation of a 2HDM, the input parameters are and ).
The Higgs particles are considered Standard Model fields, since a
2HDM is a straightforward extension of the Standard Model. The MSSM Higgs
sector is more complicated than that described above in
section , and includes important radiative corrections to
the tree-level relations. The CP-even Higgs mixing angle is
shifted as well as the full Higgs mass spectrum. The properties of the
radiatively-corrected Higgs sector in PYTHIA are derived in the effective
potential approach [Car95]. The effective potential contains an
all-orders resummation of the most important radiative corrections, but
makes approximations to the virtuality of internal propagators. This is to
be contrasted with the diagrammatic technique, which performs a fixed-order
calculation without approximating propagators. In practice, both techniques
can be systematically corrected for their respective approximations, so that
there is good agreement between their predictions, though sometimes the
agreement occurs for slightly different values of SUSY-breaking
parameters. The calculation of the Higgs spectrum in PYTHIA
is based on the `FORTRAN` code `SubHpole` [Car95],
which is also used in `HDecay` [Djo97], except that certain
corrections that are particularly important at large values of
are included rigorously in PYTHIA.

There are several notable properties of the MSSM Higgs sector. As long as the soft SUSY-breaking parameters are less than about 1.5 TeV, a number which represents a fair, albeit subjective, limit for where the required degree of fine-tuning of MSSM parameters becomes unacceptably large, there is an upper bound of about 135 GeV on the mass of the CP-even Higgs boson most like the Standard Model one, i.e. the one with the largest couplings to the and bosons, be it the or . If it is that is the SM-like Higgs boson, then can be significantly heavier. On the other hand, if is the SM-like Higgs boson, then must be even lighter. If all SUSY particles are heavy, but is small, then the low-energy theory would look like a two-Higgs-doublet model. For sufficiently large , the heavy Higgs doublet decouples, and the effective low-energy theory has only one light Higgs doublet with SM-like couplings to gauge bosons and fermions.

The Standard Model fermion masses are not fixed by SUSY,
but their Yukawa couplings become
a function of .
For the up- and down-quark and leptons,
,
, and
,
where
is the corresponding Yukawa coupling and GeV is the
order parameter of Electroweak symmetry breaking.
At large , significant corrections can occur
to these relations. These are included for the quark,
which appears to have the most sensitivity to them, and
the quark in the subroutine
`PYPOLE`, based on an updated version of `SubHpole`,
which also includes some bug fixes, so that
it is generally better behaved.
The array values `RMSS(40)` and `RMSS(41)` are used for
temporary storage of the corrections
and
.

The input parameters that determine the MSSM Higgs sector
in PYTHIA are `RMSS(5)` (), `RMSS(19)` (
),
`RMSS(10-12)` (the third generation squark mass parameters),
`RMSS(15-16)` (the third generation squark trilinear
couplings), and `RMSS(4)` (the Higgsino mass ).
Additionally, the large corrections related
to the Yukawa coupling depend on `RMSS(3)`
(the gluino mass).
Of course, these calculations also
depend on SM parameters (
etc.). Any
modifications to these quantities from virtual MSSM effects are not
taken into account. In principle, the sparticle masses also acquire
loop corrections that depend on all MSSM masses.

If `IMSS(4) = 0`, an approximate version of the effective potential
calculation can be used. It is not as accurate as that available for
`IMSS(4) = 1`, but it useful for demonstrating the effects of higher
orders. Alternatively, for `IMSS(4) = 2`, the physical Higgs masses
are set by their `PMAS` values while the CP-even Higgs boson mixing
angle is set by `RMSS(18)`. These values and
(`RMSS(5)`) are enough to determine the couplings, provided that
the same tree-level relations are used.

See section for a description how to use the loop-improved RGE's of ISASUSY to determine the SUSY mass and mixing spectrum (including also loop corrections to the Higgs mass spectrum and couplings) with PYTHIA.

Finally, a run-time interface to FEYNHIGGS [Hei99],
for the diagrammatic calculation of the , , , and
masses and the mixing angle in the MSSM, has been introduced,
available through the option `IMSS(4) = 3`. For the time being, it can
be invoked either when using an SLHA SUSY spectrum, i.e. for
`IMSS(1) = 11`, or when using the run-time interface to ISASUSY,
i.e. for `IMSS(1) = 12` or 13. The interface calls three
`FeynHiggs` routines, in the following order:

`FHSETFLAGS(IERR,4,0,0,2,0,2,1,1) :`these are the `default' settings recommended for FEYNHIGGS [Hei99].`FHSETPARA :`to set the MSSM parameters.`FHHIGGSCORR :`to get the corrected Higgs parameters.