Asymmetries and polarization measurements at the Z peak

In many ways one of the most characteristic features of the SM is the parity-violating coupling of the Z° to fermions [(see eqns (5.1.3)-(5.1.9)]. It is thus of great importance to have an accurate measurement of v and a. As is clear from (8.6.10) or (8.6.12) the Z° leptonic partial widths, or equivalently e+e — U cross-sections, only yield information on the combination vf 4- af) or vf -I- af) if one uses the higher order result (8.5.24). 

Recall that firom (5.1.6) the vector coupling Vg 8i id Ve of the leptons is very small, so that also the Ai are very small. For sin 0iv = 0.23 we estimate A = AfiC 0.16 implying a tiny asymmetry i4pB 1.9%. This is borne out in the data of Fig. 8.20 (L3, 1990c) which corresponds to Afb = (2.52 0.06)%. 

Now for a given experimental error 6Ape in the measured asymmetry we have from (8.8.2) 

We shall now demonstrate how experiments with longitudinally polarized e beams could lead to a much more accurate measurement of qv,a-For simplicity we deal just with Z exchange. 

Let Ve and be the degree of longitudinal polarization of the e and e beams. Then the relative numbers of right- and left-handed particles 

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