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Extended neutral Higgs sector

MSEL = 19
$\mathrm{h}^0$ $\H ^0$ $\mathrm{A}^0$  
3 151 156 $\mathrm{f}_i \overline{\mathrm{f}}_i \to X$
102 152 157 $\mathrm{g}\mathrm{g}\to X$
103 153 158 $\gamma \gamma \to X$
111 183 188 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}X$
112 184 189 $\mathrm{q}\mathrm{g}\to \mathrm{q}X$
113 185 190 $\mathrm{g}\mathrm{g}\to \mathrm{g}X$
24 171 176 $\mathrm{f}_i \overline{\mathrm{f}}_i \to \mathrm{Z}^0 X$
26 172 177 $\mathrm{f}_i \overline{\mathrm{f}}_j \to \mathrm{W}^+ X$
123 173 178 $\mathrm{f}_i \mathrm{f}_j \to \mathrm{f}_i \mathrm{f}_j X$ ( $\mathrm{Z}\mathrm{Z}$ fusion)
124 174 179 $\mathrm{f}_i \mathrm{f}_j \to \mathrm{f}_k \mathrm{f}_l X$ ( $\mathrm{W}^+ \mathrm{W}^-$ fusion)
121 181 186 $\mathrm{g}\mathrm{g}\to \mathrm{Q}_k \overline{\mathrm{Q}}_k X$
122 182 187 $\mathrm{q}_i \overline{\mathrm{q}}_i \to \mathrm{Q}_k \overline{\mathrm{Q}}_k X$

In PYTHIA, the particle content of a two-Higgs-doublet scenario is included: two neutral scalar particles, 25 and 35, one pseudoscalar one, 36, and a charged doublet, $\pm 37$. (Of course, these particles may also be associated with corresponding Higgs states in larger multiplets.) By convention, we choose to call the lighter scalar Higgs $\mathrm{h}^0$ and the heavier $\H ^0$. The pseudoscalar is called $\mathrm{A}^0$ and the charged $\H ^{\pm}$. Charged-Higgs production is covered in section [*].

A number of $\mathrm{h}^0$ processes have been duplicated for $\H ^0$ and $\mathrm{A}^0$. The correspondence between ISUB numbers is shown in the table above: the first column of ISUB numbers corresponds to $X = \mathrm{h}^0$, the second to $X = \H ^0$, and the third to $X = \mathrm{A}^0$. Note that several of these processes are not expected to take place at all, owing to vanishing Born term couplings. We have still included them for flexibility in simulating arbitrary couplings at the Born or loop level, or for the case of mixing between the scalar and pseudoscalar sectors.

A few Standard Model Higgs processes have no correspondence in the scheme above. These include

5 and 8, which anyway have been superseded by 123 and 124;
71, 72, 73, 76 and 77, which deal with what happens if there is no light Higgs, and so is a scenario complementary to the one above, where several light Higgs bosons are assumed; and
110, which is mainly of interest in Standard Model Higgs searches.

The processes 102-103, 111-113, 152-153, 157-158, 183-185 and 188-190 have only been worked out in full detail for the Standard Model Higgs case, and not when other (e.g. squark loop) contributions need be considered. For processes 102-103, 152-153, and 157-158, the same approximation mainly holds true for the decays, since these production processes are proportional to the partial decay width for the $\mathrm{g}\mathrm{g}$ and $\gamma\gamma$ channels. The $\gamma\gamma$ channel does include $\H ^+$ in the loop. In some corners of SUSY parameter space, the effects of squarks and gauginos in loops can be relevant. The approximate procedure outlined in section [*], based on combining the kinematics shape from simple expressions in the $m_{\t } \to \infty$ limit with a normalization derived from the $\mathrm{g}\mathrm{g}\to X$ cross section, should therefore be viewed as a first ansatz only. In particular, it is not recommended to try the non-default MSTP(38) = 0 option, which is incorrect beyond the Standard Model.

In processes 121, 122, 181, 182, 186 and 187 the recoiling heavy flavour is assumed to be top, which is the only one of interest in the Standard Model, and the one where the parton-distribution-function approach invoked in processes 3, 151 and 156 is least reliable. However, it is possible to change the quark flavour in 121 etc.; for each process ISUB this flavour is given by KFPR(ISUB,2). This may become relevant if couplings to $\b\overline{\mathrm{b}}$ states are enhanced, e.g. if $\tan\beta \gg 1$ in the MSSM. The matrix elements in this group are based on scalar Higgs couplings; differences for a pseudoscalar Higgs remains to be worked out, but are proportional to the heavy quark mass relative to other kinematic quantities.

By default, the $\mathrm{h}^0$ has the couplings of the Standard Model Higgs, while the $\H ^0$ and $\mathrm{A}^0$ have couplings set in PARU(171) - PARU(178) and PARU(181) - PARU(190), respectively. The default values for the $\H ^0$ and $\mathrm{A}^0$ have no deep physics motivation, but are set just so that the program will not crash due to the absence of any couplings whatsoever. You should therefore set the above couplings to your desired values if you want to simulate either $\H ^0$ or $\mathrm{A}^0$. Also the couplings of the $\mathrm{h}^0$ particle can be modified, in PARU(161) - PARU(165), provided that MSTP(4) = 1.

For MSTP(4) = 2, the mass of the $\mathrm{h}^0$ (PMAS(25,1)) and the $\tan\beta$ value (PARU(141)) are used to derive the masses of the other Higgs bosons, as well as all Higgs couplings. PMAS(35,1) - PMAS(37,1) and PARU(161) - PARU(195) are overwritten accordingly. The relations used are the ones of the Born-level MSSM [Gun90].

Note that not all combinations of $m_{\mathrm{h}}$ and $\tan\beta$ are allowed; for MSTP(4) = 2 the requirement of a finite $\mathrm{A}^0$ mass imposes the constraint

m_{\mathrm{h}} < m_{\mathrm{Z}} \, \frac{\tan^2\beta - 1}{\tan^2\beta + 1},
\end{displaymath} (136)

or, equivalently,
\tan^2\beta > \frac{m_{\mathrm{Z}} + m_{\mathrm{h}}}{m_{\mathrm{Z}} - m_{\mathrm{h}}}.
\end{displaymath} (137)

If this condition is not fulfilled, the program will print a diagnostic message and stop.

A more realistic approach to the Higgs mass spectrum is to include radiative corrections to the Higgs potential. Such a machinery has never been implemented as such in PYTHIA, but appears as part of the Supersymmetry framework described in sections [*] and [*]. At tree level, the minimal set of inputs would be IMSS(1) = 1 to switch on SUSY, RMSS(5) to set the $\tan\beta$ value (this overwrites the PARU(141) value when SUSY is switched on) and RMSS(19) to set $\mathrm{A}^0$ mass. However, the significant radiative corrections depend on the properties of all particles that couple to the Higgs boson, and the user may want to change the default values of the relevant RMSS inputs. In practice, the most important are those related indirectly to the physical masses of the third generation supersymmetric quarks and the Higgsino: RMSS(10) to set the left-handed doublet SUSY mass parameter, RMSS(11) to set the right stop mass parameter, RMSS(12) to set the right sbottom mass parameter, RMSS(4) to set the Higgsino mass and a portion of the squark mixing, and RMSS(16) and RMSS(17) to set the stop and bottom trilinear couplings, respectively, which specifies the remainder of the squark mixing. From these inputs, the Higgs masses and couplings would be derived. Note that switching on SUSY also implies that Supersymmetric decays of the Higgs particles become possible if kinematically allowed. If you do not want this to happen, you may want to increase the SUSY mass parameters. (Use CALL PYSTAT(2) after initialization to see the list of branching ratios.)

Pair production of Higgs states may be a relevant source, see section [*] below.

Finally, heavier Higgs bosons may decay into lighter ones, if kinematically allowed, in processes like $\mathrm{A}^0 \to \mathrm{Z}^0 \mathrm{h}^0$ or $\H ^+ \to \mathrm{W}^+ \mathrm{h}^0$. Such modes are included as part of the general mixture of decay channels, but they can be enhanced if the uninteresting channels are switched off.

next up previous contents
Next: Charged Higgs sector Up: Higgs Production Previous: Heavy Standard Model Higgs   Contents
Stephen Mrenna 2007-10-30