Heavy Standard Model Higgs

ISUB =

5	$\mathrm{Z}^0 \mathrm{Z}^0 \to \mathrm{h}^0$
8	$\mathrm{W}^+ \mathrm{W}^- \to \mathrm{h}^0$
71	$\mathrm{Z}^0 \mathrm{Z}^0 \to \mathrm{Z}^0 \mathrm{Z}^0$ (longitudinal)
72	$\mathrm{Z}^0 \mathrm{Z}^0 \to \mathrm{W}^+ \mathrm{W}^-$ (longitudinal)
73	$\mathrm{Z}^0 \mathrm{W}^+ \to \mathrm{Z}^0 \mathrm{W}^+$ (longitudinal)
76	$\mathrm{W}^+ \mathrm{W}^- \to \mathrm{Z}^0 \mathrm{Z}^0$ (longitudinal)
77	$\mathrm{W}^+ \mathrm{W}^{\pm} \to \mathrm{W}^+ \mathrm{W}^{\pm}$ (longitudinal)

Processes 5 and 8 are the simple $2 \to 1$ versions of what is now available in 123 and 124 with the full $2 \to 3$ kinematics. For low Higgs masses processes 5 and 8 overestimate the correct cross sections and should not be used, whereas good agreement between the $2 \to 1$ and $2 \to 3$ descriptions is observed when heavy Higgs production is studied.

The subprocesses 5 and 8, $V V \to \mathrm{h}^0$, which contribute to the processes $V V \to V' V'$, show a bad high-energy behaviour. Here $V$ denotes a longitudinal intermediate gauge boson, $\mathrm{Z}^0$ or $\mathrm{W}^{\pm}$. This can be cured only by the inclusion of all $V V \to V' V'$ graphs, as is done in subprocesses 71, 72, 73, 76 and 77. In particular, subprocesses 5 and 8 give rise to a fictitious high-mass tail of the Higgs. If this tail is thrown away, however, the agreement between the $s$-channel graphs only (subprocesses 5 and 8) and the full set of graphs (subprocesses 71 etc.) is very good: for a Higgs of nominal mass 300 (800) GeV, a cut at 600 (1200) GeV retains 95% (84%) of the total cross section, and differs from the exact calculation, cut at the same values, by only 2% (11%) (numbers for SSC energies). With this prescription there is therefore no need to use subprocesses 71 etc. rather than subprocesses 5 and 8.

For subprocess 77, there is an option, see MSTP(45), to select the charge combination of the scattering $\mathrm{W}$'s: like-sign, opposite-sign (relevant for Higgs), or both.

Process 77 contains a divergence for $p_{\perp}\to 0$ due to $\gamma$-exchange contributions. This leads to an infinite total cross section, which is entirely fictitious, since the simple parton-distribution function approach to the longitudinal $\mathrm{W}$ flux is not appropriate in this limit. For this process, it is therefore necessary to make use of a cut, e.g. $p_{\perp}> m_{\mathrm{W}}$.

For subprocesses 71, 72, 76 and 77, an option is included (see MSTP(46)) whereby you can select only the $s$-channel Higgs graph; this will then be essentially equivalent to running subprocess 5 or 8 with the proper decay channels (i.e. $\mathrm{Z}^0 \mathrm{Z}^0$ or $\mathrm{W}^+ \mathrm{W}^-$) set via MDME. The difference is that the Breit-Wigners in subprocesses 5 and 8 contain a mass-dependent width, whereas the width in subprocesses 71-77 is calculated at the nominal Higgs mass; also, higher-order corrections to the widths are treated more accurately in subprocesses 5 and 8. Further, processes 71-77 assume the incoming $\mathrm{W}/ \mathrm{Z}$ to be on the mass shell, with associated kinematics factors, while processes 5 and 8 have $\mathrm{W}/ \mathrm{Z}$ correctly space-like. All this leads to differences in the cross sections by up to a factor of 1.5.

In the absence of a Higgs, the sector of longitudinal $\mathrm{Z}$ and $\mathrm{W}$ scattering will become strongly interacting at energies above 1 TeV. The models proposed by Dobado, Herrero and Terron [Dob91] to describe this kind of physics have been included as alternative matrix elements for subprocesses 71, 72, 73, 76 and 77, selectable by MSTP(46). From the point of view of the general classification scheme for subprocesses, this kind of models should appropriately be included as separate subprocesses with numbers above 100, but the current solution allows a more efficient reuse of existing code. By a proper choice of parameters, it is also here possible to simulate the production of a techni-$\rho$ (see subsection ).

Currently, the scattering of transverse gauge bosons has not been included, neither that of mixed transverse-longitudinal scatterings. These are expected to be less important at high energies, and do not contain an $\mathrm{h}^0$ resonance peak, but need not be entirely negligible in magnitude. As a rule of thumb, processes 71-77 should not be used for $VV$ invariant masses below 500 GeV.

The decay products of the longitudinal gauge bosons are correctly distributed in angle.