The two animations below show how the distributions of the visible variables cos^V and cos_ll change as the average boost of Y in the LAB frame changes. The solid lines show the (immeasurable) true cos curves and the dotted lines cos^V (left) and cos_ll (right) for both a spin zero Y and a vector coupling spin half Y.
The kinematic cuts described in the paper are applied. The lowest value of beta^ave_LAB occurs when Y\bar{Y} are produced at threshold in their CM frame. Note the difference between the flat distributions of cos^V (almost flat  the cuts warp them somewhat) and the arched distributions of cos_ll, for both spin zero and spin half Y. These curves are equal, because an isotropic decay of Y and \bar{Y} is assumed.
As beta^ave_LAB increases, the decay products follow ever more closely the direction of their parent particle. The difference between cos^V and cos_ll is highlighted by how they have to change in order to follow the true cos curves (which at the highest value of beta shown, they almost perfectly do, except for the effects of the cuts). In particular, note how the starting point of the vector curve for cos_ll means that it always suffers from a pseudorapidity "dragdown" at the edges of its distribution.
