Extended neutral Higgs sector

MSEL = 19
ISUB =

$\mathrm{h}^0$	$\H ^0$	$\mathrm{A}^0$
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

$\bullet$

5 and 8, which anyway have been superseded by 123 and 124;

$\bullet$

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

$\bullet$

110, which is mainly of interest in Standard Model Higgs searches.

The processes 111-113, 183-185 and 188-190 have only been worked out in full detail for the Standard Model Higgs case, and not when e.g. squark loop contributions need be considered. The approximate procedure outlined in subsection , 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) is set to 1.

For MSTP(4)=2, the mass of the $\mathrm{h}^0$ (in PMAS(25,1)) and the $\tan\beta$ value (in 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]. Loop corrections to those expressions have been calculated within specific supersymmetric scenarios, and are known to have a non-negligible effects on the resulting phenomenology. By switching on supersymmetry simulation and setting parameters appropriately, one will gain access to these mass formulae, see section .

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

$$m_{\mathrm{h}} < m_{\mathrm{Z}} \, \frac{\tan^2\beta - 1}{\tan^2\beta + 1},$$ (137)

or, equivalently,

$$\tan^2\beta > \frac{m_{\mathrm{Z}} + m_{\mathrm{h}}}{m_{\mathrm{Z}} - m_{\mathrm{h}}}.$$ (138)

If this condition is not fulfilled, the program will crash.

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 subsection . 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.