I am indeed only talking about theoretical predictions. Showing that various hypotheses (all in agreement with current data) for the beyond the Standard Model setup give predictions that can be potentially distinguishable from each other.

Going back to the figure, let's start with the caption below (the collision in the Oxyz frame). The two protons collide following the Oz axis. They will fragment in strongly interacting pieces that will radiate and decay so that the z-direction will be full of particles. Any measurement along this direction is thus impossible. That is why we are focusing on what is happening in the transverse plane (the Oxy plane). Our process is
p p > W H > (l vl) (b b~)
The W decays into a lepton (l) and a neutrino (vl). The Higgs boson decays into a bottom (b) - antibottom (b~) pair. As we cannot measure anything following the Oz direction, we will project the momentum of the decay products in the Oxy plane. The transverse momentum is the norm of this 2D vector:
pt = sqrt(px^2 + py^2)
and pz is not measured. Is it clearer?

Thanks for the corrections ;)