Before modifying guinea-pig so that all four components of the electrons' and positrons' momenta were available, several approaches were tried to analyse statistical correlations involving the z-magnitudes of the momenta: the sum of the momenta, Σp, and the momentum loss, Δp. These relied on the fact that the outgoing particles are nearly collinear.
An estimate of the true centre of mass energy can be obtained by saying
√Sest = 2pnominal - Δp
√Strue = p1 + p2
As often, p1+p2 is used as an approximation for the centre of mass energy; but we find that this leads to a small offset in at low energies: it is preferable to use √p1p2 as an estimate for √S (as, by definition, S = 2p1p2 – 2p1.p2 and the 3-vector dot product can be neglected due to small angle.)