The associative production with a W vector boson was first mentioned
in  where the expression for the cross section in a
slightly more modern notation is
for W +H production. For the W -H production the quark fu,fd and anti-quark f,f structure functions are interchanged. The value of fW is given by the expression
For a Higgs mass of 150 GeV the production cross section is around 1 pb or 4% of the gluon fusion cross section. With the present structure functions available the uncertainty in the cross section is around 30%. However, this uncertainty can to a large extent be reduced by using single W production as a reference process . At LHC energies it is estimated that
|3.5 10- 8||(26)|
The other associative production of interest is the H t process. The cross section was first calculated by Kunszt in  with further details in . Since ten different Feynman diagrams contribute to the process just in lowest order the calculation is complicated and no derivation will be given here. For Higgs masses below 200 GeV the cross section is around a factor 5 below the cross section for associative production with a W, while for Higgs masses above 500 GeV it reaches above the WH cross section but is still far below the gluon fusion cross section.
In the case of a supersymmetric Higgs sector the cross sections for the fermionic and bosonic associative production will change in different ways from the standard model values.