  The TauSpinner algorithm allows to modify the physics of the Monte Carlo
generated samples due to the changed assumptions of event production dynamics,
without re-generating events. To each event it attributes weights: the spin
effects of tau-lepton production or decay, or the production mechanism are
modified. There is no need to repeat the detector response simulation. We
document the extension to 2 to 4 processes in which the matrix elements for the
parton-parton scattering amplitudes into a tau-lepton pair and two outgoing
partons are used. Tree-level matrix elements for the Standard Model processes,
including the Higgs boson production are used. Automatically generated codes by
MadGraph5 have been adapted. Tests of the matrix elements, reweighting
algorithm and numerical results are presented. For averaged tau lepton
polarisation, we perform comparison of 2 to 2 and 2 to 4 matrix elements used
to calculate the spin weight in pp to tau tau j j events. We show, that for
events with tau-lepton pair close to the Z-boson peak, the tau-lepton
polarisation calculated using 2 to 4 matrix elements is very close to the one
calculated using 2 to 2 Born process only. For the m_(tautau) masses above the
Z-boson peak, the effect from including 2 to 4 matrix elements is also
marginal, however when restricting into subprocesses qq,q bar q to tau tau j j
only, it can lead to a 10% difference on the predicted tau-lepton polarisation.
Choice of electroweak scheme can have significant impact. The modification of
the electroweak or strong interaction can be performed with the re-weighting
technique. TauSpinner v.2.0.0, allows to introduce non-standard couplings for
the Higgs boson and study their effects in the vector-boson-fusion. The
discussion is relegated to forthcoming publications.
