# Asymmetries at SLC

• A
Hello everybody!
I have a question regarding the measure of the asymmetry left-right (##A_{LR}##) at the SLC. Since the beam was not fully polarized the measured asymmetry is different from the theoretical one. The relation which I have found on papers and books is:
$$A_{LR}^{measured} = \frac{|N_L - N_R|}{N_L + N_R} = A_{LR} <P>$$
with ##N_L## the number of events when the beam is left-polarized and mutatis mutandis for ##N_R##.
But what I call a left-polarized beam is: ##<P>e_L + (1-<P>) e_R##
And what I call a right-polarized beam is: ##<P>e_R + (1-<P>) e_L##
With ##e_L## the number of left-polarized electrons and mutatis mutandis for ##e_R##.
If I substitute:
$$A_{LR}^{measured} = \frac{|N_L - N_R|}{N_L + N_R} = \frac{<P>e_L + (1-<P>) e_R - <P>e_R - (1-<P>) e_L}{<P>e_L + (1-<P>) e_R + <P>e_R + (1-<P>) e_L}$$
Doing a bit of algebra I obtain:
$$A_{LR}^{measured} = \frac{e_L - e_R}{e_L + e_R} (2<P> + 1) = A_{LR} (2<P> +1)$$
which is not the relation mentioned above that I find on books...... In which point my reasoning fail?