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Extended Higgs Sector

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 $\tan\beta$, and the pseudoscalar mass $M_{\mathrm{A}}$ (as noted earlier, for the non-SUSY implementation of a 2HDM, the input parameters are $M_\mathrm{h}$ and $\tan\beta$). 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 $\alpha$ 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 $\tan\beta$ 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 $\mathrm{W}$ and $\mathrm{Z}$ bosons, be it the $\mathrm{h}$ or $\H $. If it is $\mathrm{h}$ that is the SM-like Higgs boson, then $\H $ can be significantly heavier. On the other hand, if $\H $ is the SM-like Higgs boson, then $\mathrm{h}$ must be even lighter. If all SUSY particles are heavy, but $M_{\mathrm{A}}$ is small, then the low-energy theory would look like a two-Higgs-doublet model. For sufficiently large $M_{\mathrm{A}}$, 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 $\tan\beta$. For the up- and down-quark and leptons, $m_u = h_u v \sin \beta$, $m_d = h_d v \cos \beta$, and $m_\ell = h_\ell v \cos \beta$, where $h_{f=u,d,\ell}$ is the corresponding Yukawa coupling and $v \approx 246$ GeV is the order parameter of Electroweak symmetry breaking. At large $\tan\beta$, significant corrections can occur to these relations. These are included for the $\b $ quark, which appears to have the most sensitivity to them, and the $\t $ 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 $\Delta m_{\t }$ and $\Delta m_{\b }$.

The input parameters that determine the MSSM Higgs sector in PYTHIA are RMSS(5) ($\tan\beta$), RMSS(19) ( $M_{\mathrm{A}}$), RMSS(10-12) (the third generation squark mass parameters), RMSS(15-16) (the third generation squark trilinear couplings), and RMSS(4) (the Higgsino mass $\mu$). Additionally, the large $\tan\beta$ corrections related to the $\b $ Yukawa coupling depend on RMSS(3) (the gluino mass). Of course, these calculations also depend on SM parameters ( $m_{\t }, m_{\mathrm{Z}}, \alpha_{\mathrm{s}},$ 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 $\alpha$ is set by RMSS(18). These values and $\tan\beta$ (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 $\mathrm{h}^0$, $\H ^0$, $\mathrm{A}^0$, and $\H ^+$ masses and the mixing angle $\alpha$ 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:

$\bullet$
FHSETFLAGS(IERR,4,0,0,2,0,2,1,1) : these are the `default' settings recommended for FEYNHIGGS [Hei99].
$\bullet$
FHSETPARA : to set the MSSM parameters.
$\bullet$
FHHIGGSCORR : to get the corrected Higgs parameters.
Note that, for PYTHIA to compile properly without the FEYNHIGGS library, three dummy routines have been added to the PYTHIA source code, corresponding to the three listed above. To obtain proper linking with FEYNHIGGS, these dummy routines should first be removed/renamed and the PYTHIA source recompiled without them. The interface has been tested to work with FEYNHIGGS-2.2.8. Differences in the FEYNHIGGS and SubHpole predictions represent, to some degree, the theoretical uncertainty in the MSSM Higgs sector.


next up previous contents
Next: Superpartners of Gauge and Up: Supersymmetry Previous: General Introduction   Contents
Stephen Mrenna 2007-10-30